Juan J. Alonso

Stanford University Unstructured (SU 2 ): An open-source integrated computational environment for multi-physics simulation and design

This paper describes the history, objectives, structure, and current capabilities of the Stanford University Unstructured (SU 2 ) tool suite. This computational analysis and design software collection is being developed to solve complex, multi-physics analysis and optimization tasks using arbitrary unstructured meshes, and it has been designed so that it is easily extensible for the solution of Partial Differential Equation-based (PDE) problems not directly envisioned by the authors. At its core, SU 2 is an open-source collection of C++ software tools to discretize and solve problems described by PDEs and is able to solve PDE-constrained optimization problems, including optimal shape design. Although the toolset has been designed with Computational Fluid Dynamics (CFD) and aerodynamic shape optimization in mind, it has also been extended to treat other sets of governing equations including potential flow, electrodynamics, chemically reacting flows, and several others. In our experience, capabilities for computational analysis and optimization have improved considerably over the past two decades. However, the ability to integrate the resulting software packages into coupled multi-physics analysis and design optimization solvers has remained a challenge: the variety of approaches chosen for the independent components of the overall problem (flow solvers, adjoint solvers, optimizers, shape parameterization, shape deformation, mesh adaption, mesh deformation, etc) make it difficult to (a) expand the range of applicability to situations not originally envisioned, and (b) to reduce the overall burden of creating integrated applications. By leveraging well-established object-oriented software architectures (using C++) and by enabling a common interface for all the necessary components, SU 2 is able to remove these barriers for both the beginner and the seasoned analyst. In this paper we attempt to describe our efforts to develop SU 2 as an integrated platform. In some senses, the paper can also be used as a software reference manual for those who might be interested in modifying it to suit their own needs. We carefully describe the C++ framework and object hierarchy, the sets of equations that can be currently modeled by SU 2 , the available choices for numerical discretization, and conclude with a set of relevant validation and verification test cases that are included with the SU 2 distribution. We intend for SU 2 to remain open source and to serve as a starting point for new capabilities not included in SU 2 today, that will hopefully be contributed by users in both academic and industrial environments.

On Active Subspaces in Car Aerodynamics

The Active Subspace Method (ASM) is an emerging set of tools for dimensionality reduction in complex physical systems. It allows to discover low-dimensional trends in the quantity of interest by exploiting redundancies in the input variables and combining them linearly into so-called active variables. The purpose of this study is to assess the applicability and the benefit of the ASM in car aerodynamics. To that end, we apply the ASM to drag and lift computations of three different parameterized vehicle geometries of increasing complexity. We thereby assess the impact of adjoint-based gradient inaccuracies on the results of the ASM, devise and validate a methodology to apply the ASM in the absence of adjoint-based gradients, and exemplify the practical use of this methodology in car aerodynamics. For all investigated cases, the ASM reveals that a large portion of the overall variability of drag or lift is captured already by an active subspace of dimension one, thus providing physical insight into the main shape parameter dependencies. By projection into an active subspace of a suitably chosen dimension larger than one, it is demonstrated that the predictive accuracy of surrogate models for drag and lift can consistently be improved.

Multi-Fidelity Uncertainty Quantification: Application to a Vertical Axis Wind Turbine Under an Extreme Gust.

Designing better vertical axis wind turbines (VAWTs) requires considering the uncertainwind conditions they operate in and quantifying the e ect of such uncertainties. We studythe e ect of an uncertain extreme gust on the maximum forces on the blades of the VAWT.The gust is parametrized by three random variables that control its location, length andamplitude. We propose a multi- delity approach to uncertainty quanti cation that usespolynomial chaos to create an approximation to the high- delity statistics via a correctionfunction based on the di erence between high and low- delity simulations. The multi- delity method provides accurate statistics on the maximum forces for a small numberof simulations and the multi- delity statistics are consistent with the high- delity (CFD)statistics. We developed a practical method to simulate a gust, that changes its magnitudein the ow direction, in a CFD solver by combining the eld velocity method (FVM) andthe geometric conservation law (GCL). The ability to study the e ect of the gust with thehigh- delity (CFD) solver is crucial as the low- delity (blade element/vortex lattice) solverunderestimates the e ect of the gust on the maximum forces.

Managing Gradient Inaccuracies while Enhancing Optimal Shape Design Methods

gradient calculations from adjoint formulations. The key goal of these enhancements is to increase the accuracy of the solution while reducing the computational wall-time. This study is specically interested in quantifying the impact of mesh adaptation and approximate gradients from continuous adjoint methodologies while performing Gradient Based Optimization (GBO) or Surrogate Based Optimization (SBO). In the course of this work we have discovered conditions in which these various gradient methods can actually degrade the performance of the optimizer. For example, we have observed that bias errors from continuous adjoint gradients, which are traditionally acceptable for GBO methods, are not acceptable for basic SBO methods, which make a stronger assumption of objective-gradient correlation. We have also observed that applying mesh adaptation to continuous adjoint solutions can exacerbate this error enough to eect GBO convergence rates. In attempting to improve the convergence of the optimizers, we have built several approaches to better condition gradient accuracies. In one approach we lter the surface sensitivities before projecting them into a parameterized design space. In another approach, we build surrogate models capable of learning the noise of the system. This paper will present the work completed towards developing these methods, and will provide examples in the form of analytical test cases and demonstrative aerodynamic problems.

Sensitivity of the Performance of a 3-Dimensional Hypersonic Inlet to Shape Deformations

Supersonic combustion ramjets, or scramjets, have the potential to facilitate more efficient transatmospheric flight and airplane-like operations of vehicles for space access. A scramjet is an airbreathing engine which uses the compression of air over the forebody and inlet to achieve the conditions necessary for supersonic combustion, using no mechanical compressor. Understanding the effects of shape deformations due to vehicle compliance is important for the robust performance of scramjets at on-design conditions where deformations may be large and have a significant effect, for multi-point operation where the shape of the vehicle changes with the varying pressure and temperature distributions, and for ensuring a lack of sensitivity to manufacturing tolerances. This paper will focus on the effects of shape deformations on the performance of the vehicle inlet under design conditions using high-fidelity simulations as well as response surface methodology.

Comparison of reduced- and full-space algorithms for PDE-constrained optimization

PDE-constrained optimization problems are often solved using reduced-space quasi- Newton algorithms. Quasi-Newton methods are eective for problems with relatively few degrees of freedom, but their performance degrades as the problem size grows. In this paper, we compare two inexact-Newton algorithms that avoid the algorithmic scaling is- sues of quasi-Newton methods. The two inexact-Newton algorithms are distinguished by reduced-space and full-space implementations. Numerical experiments demonstrate that the full-space (or one-shot) inexact-Newton algorithm is typically the most ecient ap- proach; however, the reduced-space algorithm is an attractive compromise, because it requires less intrusion into existing solvers than the full-space approach while retaining excellent algorithmic scaling. We also highlight the importance of using inexact-Hessian- vector products in the reduced-space.

SUAVE: An Open-Source Environment Enabling Unconventional Vehicle Designs through Higher Fidelity

SUAVE is a conceptual level aircraft design environment that incorporates multiple information sources to analyze unconventional configurations. This work incorporates higherfidelity tools to build upon previous efforts where SUAVE analyzed and optimized several types of aircraft using low-fidelity methods. This is done in an automated way that incorporates three external programs. The first is OpenVSP, which is used for geometry creation, area calculation, and surface meshing. The second is Gmsh, which uses these surface meshes to create volume meshes. The third is SU2, which is used to run Euler CFD simulations. Wetted areas from OpenVSP and lift from SU2 is used to enhance SUAVE’s aerodynamic analyses. We present results for a verification case with the Onera M6 wing, then present mission results with a conventional narrow-body airliner, a supersonic jet, and a blended wing body.

Multi-fidelity Methods in Aerodynamic Robust Optimization

In order to design robust and reliable aerospace systems it is necessary to properly quantify the effect of uncertainties on the systems’ behavior. Performing a robust optimization with the highest fidelity method is desired albeit not feasible because of the prohibited computational cost associated with the many simulations needed in the optimization iterations to compute statistics of the system’s performance. Here we describe a multi-fidelity method to enable high-fidelity robust optimization. Our multi-fidelity method uses a polynomial chaos expansion constructed from the combination of a low-fidelity model and a model correction to approximate the high-fidelity statistics and the gradients of the statistics used in each optimization iteration. The model correction accounts for the difference between the high-fidelity (Computational Fluid Dynamics RANS) model and the low-fidelity (CFD Euler) model. A key feature of the multi-fidelity method is its incorporation of analytic gradients (adjoints) from the CFD to obtain the gradients of the statistics. The application of the multi-fidelity method to the robust optimization of an RAE2822 airfoil subject to uncertain flow conditions shows that 60% to 90% computational savings can be achieved when compared to the high-fidelity optimization.

Adjoint-Based Optimization of a Hypersonic Inlet

Supersonic combustion ramjets, or scramjets, have the potential to facilitate more efficient transatmospheric flight and airplane-like operations of launch vehicles. A scramjet is an airbreathing engine which uses the compression of air over the forebody and inlet to achieve the conditions necessary for supersonic combustion, using no mechanical compressor. The highly complex flow experienced by three-dimensional hypersonic inlets, demanding performance requirements, and engine design strongly coupled to the vehicle create a need for simulation-based design. Therefore, efficient high-fidelity computation of gradients is desired. In this paper, the derivation, verification, and application of an adjoint formulation for an objective relevant to thrust (ṁ) will be presented. The design problem addressed is the optimization of a simple hypersonic inlet geometry, however this method is applicable to other engineering problems.

Fuel-Burn Impact of Re-Designing Future Aircraft with Changes in Mission Specifications

Over the past few years, pressure to reduce the overall fuel consumption of the commercial aircraft eet has been growing steadily. Expenses related to fuel are now one of the largest contributors to an airline’s direct operating cost. In addition, harmful emissions derived from the engine combustion process (CO2, NOx, and others) must be signicantly reduced in order to meet future targets that the industry has set for itself. The fuel burn impact of varying design mission specications (payload, range, cruise Mach number, and allowable span) of tube and wing aircraft is studied in this paper. Representative aircraft from all groups (Regional Jet - CRJ900, Single Aisle- B737-800, Small Twin Aisle- B767300ER, Large Twin Aisle- B777-200ER, and Large Aircraft - B747-400) are chosen and redesigned for variations in the design cruise Mach number, wing span and R1 range. In addition, the eects of improvements in aerodynamic, structural and propulsion technology expected over the next 20 years are taken into account in the context of technology scenarios for which the baseline aircraft are redesigned. The eectiveness of mission specication changes in reducing the fuel burn of these technologically advanced aircraft is also observed. Results from aircraft redesigns indicate that variations in design mission specications can result in aircraft with improved fuel burn characteristics (up to a 24 percent reduction). Results also indicate that even for aircraft at higher technology levels, mission specication changes can still contribute to signicant improvement in aircraft performance.