Robert Haimes

Identification of swirling flow in 3-D vector fields

An algorithm for identifying the center of swirling flow in 3-D discretized vector fields has been developed. The algorithm is based on critical point theory and has been implemented as a visualization tool within pV3, a package for visualizing 3-D transient data. The scheme works with gridding supported by pV3: structured meshes as well as unstructured grids composed of tetrahedra, polytetrahedral strips, hexahedra, pyramids, and/or prism cells. The results have been validated using artificially-generated vector fields and 3-D CFD data.

Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping

Engineers are increasingly using high-fidelity models for numerical optimization. However, the computational cost of these models, combined with the large number of objective function and constraint evaluations required by optimization methods, can render such optimization computationally intractable. Surrogate-based optimization (SBO) optimization using a lower-fidelity model most of the time, with occasional recourse to the high-fidelity model is a proven method for reducing the cost of optimization. One branch of SBO uses lower-fidelity physics models of the same system as the surrogate. Until now however, surrogates using a different set of design variables from that of the high-fidelity model have not been available to use in a provably convergent numerical optimization. New methods are herein developed and demonstrated to reduce the computational cost of numerical optimization of variableparameterization problems, that is, problems for which the low-fidelity model uses a different set of design variables from the high-fidelity model. Four methods are presented to perform mapping between variable-parameterization spaces, the last three of which are new: space mapping, corrected space mapping, a mapping based on proper orthogonal decomposition (POD), and a hybrid between POD mapping and space mapping. These mapping methods provide links between different models of the same system and have further applications beyond formal optimization strategies. On an unconstrained airfoil design problem, it achieved up to 40% savings in highfidelity function evaluations. On a constrained wing design problem it achieved 76% time savings, and on a bat flight design problem, it achieved 45% time savings. On a large-scale practical aerospace application, such time savings could represent weeks. Thesis Supervisor: Karen Willcox Title: Associate Professor of Aeronautics and Astronautics Thesis Supervisor: Robert Haimes Title: Principal Research Engineer

Advanced interactive visualization for CFD

Abstract New ideas are presented for the visualization of computational fluid dynamics data. These include both unsteady two-dimensional and steady three-dimensional data on either structured or unstructured grids. In addition to presenting some specific algorithm advances, considerable attention is devoted to innovative interactive probes and the appropriate choice of program architecture and internal data structure.

On the velocity gradient tensor and fluid feature extraction

A 3-D Computational Fluid Dynamics flow field may contain many topological features such as vortex cores, separation surfaces, shock surfaces, and recirculation bubbles. We describe several techniques that identify these global features using local analytical tests that can applied independently to any point or cell in a vector field. These techniques draw on concepts from critical point theory and phase plane analysis and utilize the velocity gradient tensor. For this 3x3 tensor an eigen-analysis produces 3 eigenvalues. Mapping these to the complex plane produces the classification signature. Vector field topology can be used as the foundation of automated fluid feature extraction.

Validation of a numerical method for unsteady flow calculations

This paper describes and validates a numerical method for the calculation of unsteady inviscid and viscous flows. A companion paper compares experimental measurements of unsteady heat transfer on a transonic rotor with the corresponding computational results. The mathematical model is the Reynolds-averaged unsteady Navier-Stokes equations for a compressible ideal gas. Quasi-three-dimensionality is included through the use of a variable streamtube thickness. The numerical algorithm is unusual in two respects: (a) For reasons of efficiency and flexibility, it uses a hybrid Navier-Stokes/Euler method, and (b) to allow for the computation of stator/rotor combinations with arbitrary pitch ratio, a novel space-time coordinate transformation is used. Several test cases are presented to validate the performance of the computer program, UNSFLO. These include: (a) unsteady, inviscid flat plate cascade flows (b) steady and unsteady, viscous flat plate cascade flows, (c) steady turbine heat transfer and loss prediction. In the first two sets of cases comparisons are made with theory, and in the third the comparison is with experimental data.

Fully Scaled Transonic Turbine Rotor Heat Transfer Measurements

The heat transfer to an uncooled transonic singlestage turbine has been measured in a short-duration facility, which fully simulates all the nondimensional quantities of interest for fluid flow and heat transfer (Reynolds number, Prandtl number, Rossby number, temperature ratios, and corrected speed and weight flow). Data from heat flux gages about the midspan of the rotor profile, measured from d-c to more than 10 times blade passing frequency (60 kHz), are presented in both time-resolved and mean heat transfer form. These rotating blade data are compared to previously published heat transfer measurements taken at Oxford University on the same profile in a two-dimensional cascade with bar passing to simulate blade row interaction effects. The results are qualitatively quite similar at midspan. The data are also compared to a two-dimensional Navier–Stokes calculation of the blade mean section and the implications for turbine design are discussed.

High-Fidelity Aero-Structural Design Using a Parametric CAD-Based Model

This paper presents two major additions to our high-fidelity aero-structural design environment. Our framework uses high-fidelity descriptions for both the flow around the aircraft (Euler and Navier-Stokes) and for the structural displacements and stresses (a full finite-element model) and relies on a coupled-adjoint sensitivity analysis procedure to enable the simultaneous design of the shape of the aircraft and its underlying structure to satisfy the measure of performance of interest. The first of these additions is a direct interface to a parametric CAD model that we call AEROSURF and that is based on the CAPRI Application Programming Interface (API). This CAD interface is meant to facilitate designs involving complex geometries where multiple surface intersections change as the design proceeds and are complicated to compute. In addition, the surface geometry information provided by this CAD-based parametric solid model is used as the common geometry description from which both the aerodynamic model and the structural representation are derived. The second portion of this work involves the use of the Finite Element Analysis Program (FEAP) for the structural analyses and optimizations. FEAP is a full-purpose finite element solver for structural models which has been adapted to work within our aero-structural framework. In addition, it is meant to represent the state-of-the-art in finite element modeling and it is used in this work to provide realistic aero-structural optimization costs for structural models of sizes typical in aircraft design applications. The capabilities of these two major additions are presented and discussed. The parametric CAD-based geometry engine, AEROSURF, is used in aerodynamic shape optimization and its performance is compared with our standard, in-house, geometry model. The FEAP structural model is used in optimizations using our previous version of AEROSURF (developed in-house) and is shown to provide realistic results with detailed structural models.

A CAD-Free and a CAD-Based Geometry Control System for Aerodynamic Shape Optimization

The performance of an aerodynamic shape optimization routine is greatly dependent on its geometry control system. This system must accurately parameterize the initial geometry and generate a flexible set of design variables for the optimization cycle. It must also generate new instances of the geometry based on the changes to the design variables dictated by the optimization routine. In response to changes in the geometry, it is also desirable to generate a new surface grid with the same topology as the original grid. This new surface grid can be used to perturb the associated volume grid. This paper presents two geometry control systems, a CAD-free system, and a CATIA V5 CAD-based system. The two systems provide practical tools for aerodynamic optimization. They also provide a basis for comparing CAD-free and CAD-based systems and understanding additional issues that need to be addressed in order to develop reliable optimization systems.

Multifidelity Optimization for Variable-Complexity Design

Surrogate-based-optimization methods provide a means to minimize expensive highfidelity models at reduced computational cost. The methods are useful in problems for which two models of the same physical system exist: a high-fidelity model which is accurate and expensive, and a low-fidelity model which is less costly but less accurate. A number of model management techniques have been developed and shown to work well for the case in which both models are defined over the same design space. However, many systems exist with variable fidelity models for which the design variables are defined over different spaces, and a mapping is required between the spaces. Previous work showed that two mapping methods, corrected space mapping and POD mapping, used in conjunction with a trust-region model management method, provide improved performance over conventional non-surrogate-based optimization methods for unconstrained problems. This paper extends that work to constrained problems. Three constraint-management methods are demonstrated with each of the mapping methods: Lagrangian minimization, an sequential quadratic programming-like surrogate method, and MAESTRO. The methods are demonstrated on a fixed-complexity analytical test problem and a variable-complexity wing design problem. The SQP-like method consistently outperformed optimization in the high-fidelity space and the other variable complexity methods. Corrected space mapping performed slightly better on average than POD mapping. On the wing design problem, the combination of the SQP-like method and corrected space mapping achieved 58% savings in high-fidelity function calls over optimization directly in the high-fidelity space.

Automatic vortex core detection

This case study presents applications of the eigenvector method to recent aeronautical studies at NASA Ames Research Center and Rensselaer Polytechnic Institute. We highlight its usefulness for detecting flow features such as vortex cores, vortex bursts, spiral vortex breakdowns, and vortex diffusion. The eigenvector method has also been used as a data analysis tool to guide an automatic mesh refinement program and improve the accuracy of a rotorcraft simulation.