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NASA NTRS2003

An Overview of the Materials Science Research at the Marshall Space Flight Center Electrostatic Levitator Facility and Recent CDDF Efforts

Containerless processing is an important tool for materials research. The freedom from a crucible allows processing of liquid materials in a metastable undercooled state, as well as allowing processing of high temperature and highly reactive melts. Electrostatic levitation (ESL) is a containerless method which provides a number of unique advantages, including the ability to process non-conducting materials, the ability to operate in ultra-high vacuum or at moderate gas pressure (approx. = 5 atm), and the decoupling of positioning force from sample heating. ESL also has the potential to reduce internal flow velocities below those possible with electromagnetic, acoustic, or aero-acoustic techniques. In electrostatic levitation, the acceleration of gravity (or residual acceleration in reduced gravity) is opposed by the action of an applied electric field on a charged sample. Microgravity allows electrostatic levitation to work even more effectively. The ESL facility at NASA s Marshall Space Flight Center is in use for materials research and thermophysical property measurement by a number of different internal and external investigators. Results from the recent CDDF studies on the high energy X-ray beamline at the Advanced Photon Source of Argonne National Laboratory will be presented. The Microgravity Research Program supports the facility.

Source record↗

NASA NTRS2004

Adjoint Formulation for an Embedded-Boundary Cartesian Method

Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation.

Nemec, Marian↗

NASA NTRS2003

Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy

Several current brain imaging techniques rest on the assumption of a tight coupling between neural activity and hemodynamic response. The nature of this neurovascular coupling, however, is not completely understood. There is some evidence for a decoupling of these processes at the onset of neural activity, which manifests itself as a momentary increase in the relative concentration of deoxyhemoglobin (HbR). The existence of this early component of the hemodynamic response function, however, is controversial, as it is inconsistently found. Near infrared spectroscopy (NIRS) allows quantification of levels of oxyhemoglobin (HbO(2)) and HbR during task performance in humans. We acquired NIRS data during performance of simple motor and visual tasks, using rapid-presentation event-related paradigms. Our results demonstrate that rapid, event-related NIRS can provide robust estimates of the hemodynamic response without artifacts due to low-frequency signal components, unlike data from blocked designs. In both the motor and visual data the onset of the increase in HbO(2) occurs before HbR decreases, and there is a poststimulus undershoot. Our results also show that total blood volume (HbT) drops before HbO(2) and undershoots baseline, raising a new issue for neurovascular models. We did not find early deoxygenation in the motor data using physiologically plausible values for the differential pathlength factor, but did find one in the visual data. We suggest that this difference, which is consistent with functional magnetic resonance imaging (fMRI) data, may be attributable to different capillary transit times in these cortices.

NASA Program Biomedical Research and Countermeasur↗

NASA NTRS2003

Ventricular filling slows epicardial conduction and increases action potential duration in an optical mapping study of the isolated rabbit heart

INTRODUCTION: Mechanical stimulation can induce electrophysiologic changes in cardiac myocytes, but how mechanoelectric feedback in the intact heart affects action potential propagation remains unclear. METHODS AND RESULTS: Changes in action potential propagation and repolarization with increased left ventricular end-diastolic pressure from 0 to 30 mmHg were investigated using optical mapping in isolated perfused rabbit hearts. With respect to 0 mmHg, epicardial strain at 30 mmHg in the anterior left ventricle averaged 0.040 +/- 0.004 in the muscle fiber direction and 0.032 +/- 0.006 in the cross-fiber direction. An increase in ventricular loading increased average epicardial activation time by 25%+/- 3% (P < 0.0001) and correspondingly decreased average apparent surface conduction velocity by 16%+/- 7% (P = 0.007). Ventricular loading did not significantly alter action potential duration at 20% repolarization (APD20) but did at 80% repolarization (APD80), from 179 +/- 7 msec to 207 +/- 5 msec (P < 0.0001). The dispersion of APD20 was decreased with loading from 19 +/- 2 msec to 13 +/- 2 msec (P = 0.024), whereas the dispersion of APD80 was not significantly changed. These electrophysiologic changes with ventricular loading were not affected by the nonspecific stretch-activated channel blocker streptomycin (200 microM) and were not attributable to changes in myocardial perfusion or the presence of an electromechanical decoupling agent (butanedione monoxime) during optical mapping. CONCLUSION: Acute loading of the left ventricle of the isolated rabbit heart decreased apparent epicardial conduction velocity and increased action potential duration by a load-dependent mechanism that may not involve stretch-activated channels.

NASA Program Biomedical Research and Countermeasur↗

NASA NTRS1999

Analysis of peg formation in cucumber seedlings grown on clinostats and in a microgravity (space) environment

In young cucumber seedlings, the peg is a polar out-growth of tissue that functions by snagging the seed coat, thereby freeing the cotyledons. Previous studies have indicated that peg formation is gravity dependent. In this study we analyzed peg formation in cucumber seedlings (Cucumis sativus L. cv Burpee Hybrid II) grown under conditions of normal gravity, microgravity, and simulated microgravity (clinostat rotation). Seeds were germinated on the ground, in clinostats and on board the space shuttle (STS 95) for 1-2 days, frozen and subsequently examined for their stage of development, degree of hook formation, number of pegs formed, and peg morphology. The frequency of peg formation in space grown seedlings was found to be nearly identical to that of clinostat grown seedlings and to differ from that of seedlings germinated under normal gravity only in a minority of cases; approximately 6% of the seedlings formed two pegs and nearly 2% of the seedlings lacked pegs, whereas such abnormalities did not occur in ground controls. The degree of hook formation was found to be less pronounced for space grown seedlings, compared to clinostat grown seedlings, indicating a greater degree of decoupling between peg formation and hook formation in space. Nonetheless, in all seedlings having single pegs and a hook, the peg was found to be positioned correctly on the inside of the hook, showing that there is coordinate development even in microgravity environments. Peg morphologies were altered in space grown samples, with the pegs having a blunt appearance and many pegs showing alterations in expansion, with the peg extending out over the edges of the seed coat and downwards. These phenotypes were not observed in clinostat or ground grown seedlings.

STS-95 Shuttle Project↗

NASA NTRS2004

Control of a High Speed Flywheel System for Energy Storage in Space Applications

A novel control algorithm for the charge and discharge modes of operation of a flywheel energy storage system for space applications is presented. The motor control portion of the algorithm uses sensorless field oriented control with position and speed estimates determined from a signal injection technique at low speeds and a back EMF technique at higher speeds. The charge and discharge portion of the algorithm use command feed-forward and disturbance decoupling, respectively, to achieve fast response with low gains. Simulation and experimental results are presented demonstrating the successful operation of the flywheel control up to the rated speed of 60,000 rpm.

Kenny, Barbara H.↗

NASA NTRS2005

Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all red-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principle formulation of bounded rationality and a set of new types of mean field theory in statistical physics; it also shows that those topics are fundamentally one and the same.

Wolpert, David H.↗

NASA NTRS2004

Finding Bounded Rational Equilibria: Iterative Focusing - Part 1

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality characterizing all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. It has recently been shown that the same information theoretic mathematical structure, known as Probability Collectives (PC) underlies both issues. This relationship between statistical physics and game theory allows techniques and insights from the one field to be applied to the other. In particular, PC provides a formal model-independent definition of the degree of rationality of a player and of bounded rationality equilibria. This pair of papers extends previous work on PC by introducing new computational approaches to effectively find bounded rationality equilibria of common-interest (team) games.

Wolpert, David H.↗

NASA NTRS2004

Finding Bounded Rational Equilibria: Alternative Lagrangians and Uncountable Move Spaces - Part 2

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality characterizing all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. It has recently been shown that the same information theoretic mathematical structure, known as Probability Collectives (PC) underlies both issues. This relationship between statistical physics and game theory allows techniques and insights &om the one field to be applied to the other. In particular, PC provides a formal model-independent definition of the degree of rationality of a player and of bounded rationality equilibria. This pair of papers extends previous work on PC by introducing new computational approaches to effectively find bounded rationality equilibria of common-interest (team) games.

Wolpert, David H.↗

NASA NTRS2003

The Chemical Composition and Gas-to-Dust Mass Ratio of Nearby Interstellar Matter

We use recent results on interstellar gas toward nearby stars and interstellar by-products within the solar system to select among the equilibrium radiative transfer models of the nearest interstellar material presented in Slavin & Frisch. For the assumption that O/H - 400 parts per million, models 2 and 8 are found to yield good fits to available data on interstellar material inside and outside of the heliosphere, with the exception of the Ne abundance in the pickup ion and anomalous cosmic-ray populations. For these models, the interstellar medium (ISM) at the entry point to the heliosphere has n(H(sup 0)) = 0.202-0.208/cu cm, n(He(sup 0) = 0.0137-0.0152/cu cm, and ionizations X(H) = 0.29-0.30, X(He) = 0.47-0.51. These best models suggest that the chemical composition of the nearby ISM is approx.60%-70% subsolar if S is undepleted. Both H(0) and H(+) need to be included when evaluating abundances of ions found in warm diffuse clouds. Models 2 and 8 yield an H filtration factor of approx.0.46. Gas-to-dust mass ratios for the ISM toward epsilon CMa are R(sub gd) = 178-183 for solar abundances of Holweger or R(sub gd) = 611-657 for an interstellar abundance standard 70% solar. Direct observations of dust grains in the solar system by Ulysses and Galileo yield R(sub gd) appr0x. 115 for models 2 and 8, supporting earlier results (Frisch and coworkers). If the local ISM abundances are subsolar, then gas and dust are decoupled over small spatial scales. The inferred variation in R(sub gd) over parsec length scales is consistent with the fact that the ISM near the Sun is part of a dynamically active cluster of cloudlets flowing away from the Sco-Cen association. Observations toward stars within approx.500 pc show that R(sub gd) correlates with the percentage of the dust mass that is carried by iron, suggesting that an Fe-rich grain core (by mass) remains after grain destruction. Evidently large dust grains (>10(exp -13) g) and small dust grains (<10(exp -13) g) are not well mixed over parsec length spatial scales in the ISM. It also appears that very small C-dominated dust grains have been destroyed in the ISM within several parsecs of the Sun, since C appears to be essentially undepleted. However, if gas-dust coupling breaks down over the cloud lifetime, the missing mass arguments applied here to determine R(sub gd) and dust grain mineralogy are not appropriate.

Frisch, Priscilla C.↗

NASA NTRS2004

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

Nemec, Marian↗

NASA NTRS2001

Cross-Axis Proportional Gains Used to Control Gyroscopic Effects in a Magnetic- Bearing-Supported Flywheel

For magnetic-bearing-supported high-speed machines with significant gyroscopic effects, it is necessary to stabilize both forward and backward tilt whirling modes. Instability or the low damping of these modes can prevent the attainment of desired shaft speeds. Previous work elsewhere showed that cross-axis derivative gain in the magnetic bearing control law can improve the stability of the forward whirl mode, but it is commonly recognized that derivative gains amplify high-frequency noise and increase the required control effort. At the NASA Glenn Research Center, it has been shown previously that a simple cross-axis proportional gain can add stability (without adding noise) to either forward whirl or backward whirl, depending on the sign of the gain, but that such a gain destabilizes the other mode. It has been predicted by Glenn analysis that both modes can be stabilized by cross-axis proportional gains by utilizing the large-frequency separation of the two modes at speeds where the gyroscopic effects are significant. We use a modal controller that decouples the tilt and center-of-mass-translation modes. Only the tilt modes exhibit speed-dependent gyroscopic effects. The key to controlling them by the present method is to stabilize the backward whirl tilt mode with the appropriate sign of cross-axis proportional gain in the control law, but to include a low-pass filter on that gain term to restrict its effect only to the low-frequency backward-whirl mode. A second cross-axis term with the opposite sign and a high-pass filter stabilizes the forward whirl, which can have a frequency one or two orders of magnitude higher than the backward whirl, permitting very independent action of the two terms. Because the physical gyroscopic torques are proportional to the spinning speed of the shaft, it is convenient to gain-schedule the cross-axis control terms by making them proportional to shaft speed. This has the added benefit of avoiding a somewhat awkward zero-speed splitting of the tilt-mode eigenvalues.

Brown, Gerald V.↗

NASA NTRS2005

Three-Dimensional Application of DAMAS Methodology for Aeroacoustic Noise Source Definition

At the 2004 AIAA/CEAS Aeroacoustic Conference, a breakthrough in acoustic microphone array technology was reported by the authors. A Deconvolution Approach for the Mapping of Acoustic Sources (DAMAS) was developed which decouples the array design and processing influence from the noise being measured, using a simple and robust algorithm. For several prior airframe noise studies, it was shown to permit an unambiguous and accurate determination of acoustic source position and strength. As a follow-on effort, this paper examines the technique for three-dimensional (3D) applications. First, the beamforming ability for arrays, of different size and design, to focus longitudinally and laterally is examined for a range of source positions and frequency. Advantage is found for larger array designs with higher density microphone distributions towards the center. After defining a 3D grid generalized with respect to the array s beamforming characteristics, DAMAS is employed in simulated and experimental noise test cases. It is found that spatial resolution is much less sharp in the longitudinal direction in front of the array compared to side-to-side lateral resolution. 3D DAMAS becomes useful for sufficiently large arrays at sufficiently high frequency. But, such can be a challenge to computational capabilities, with regard to the required expanse and number of grid points. Also, larger arrays can strain basic physical modeling assumptions that DAMAS and all traditional array methodologies use. An important experimental result is that turbulent shear layers can negatively impact attainable beamforming resolution. Still, the usefulness of 3D DAMAS is demonstrated by the measurement of landing gear noise source distributions in a difficult hard-wall wind tunnel environment.

Brooks, Thomas F.↗

NASA NTRS1997

SYNTHESIS OF NOVEL ALL-DIELECTRIC GRATING FILTERS USING GENETIC ALGORITHMS

We are concerned with the design of inhomogeneous, all dielectric (lossless) periodic structures which act as filters. Dielectric filters made as stacks of inhomogeneous gratings and layers of materials are being used in optical technology, but are not common at microwave frequencies. The problem is then finding the periodic cell's geometric configuration and permittivity values which correspond to a specified reflectivity/transmittivity response as a function of frequency/illumination angle. This type of design can be thought of as an inverse-source problem, since it entails finding a distribution of sources which produce fields (or quantities derived from them) of given characteristics. Electromagnetic sources (electric and magnetic current densities) in a volume are related to the outside fields by a well known linear integral equation. Additionally, the sources are related to the fields inside the volume by a constitutive equation, involving the material properties. Then, the relationship linking the fields outside the source region to those inside is non-linear, in terms of material properties such as permittivity, permeability and conductivity. The solution of the non-linear inverse problem is cast here as a combination of two linear steps, by explicitly introducing the electromagnetic sources in the computational volume as a set of unknowns in addition to the material unknowns. This allows to solve for material parameters and related electric fields in the source volume which are consistent with Maxwell's equations. Solutions are obtained iteratively by decoupling the two steps. First, we invert for the permittivity only in the minimization of a cost function and second, given the materials, we find the corresponding electric fields through direct solution of the integral equation in the source volume. The sources thus computed are used to generate the far fields and the synthesized triter response. The cost function is obtained by calculating the deviation between the synthesized value of reflectivity/transmittivity and the desired one. Solution geometries for the periodic cell are sought as gratings (ensembles of columns of different heights and widths), or combinations of homogeneous layers of different dielectric materials and gratings. Hence the explicit unknowns of the inversion step are the material permittivities and the relative boundaries separating homogeneous parcels of the periodic cell.

Zuffada, Cinzia↗

NASA NTRS2006

Pyroxenes in Martian meteorites as petrogenetic indicators

Pyroxenes in Martian meteorites are important recorders of petrogenetic processes. Understanding the details of pyroxene major and minor element compositional variations can provide important insights into those processes. A combination of careful petrographic analysis of natural samples and experimental crystallization studies can lead to better understanding of the processes that gave rise to these samples on Mars. In addition, experimentally determined major, minor and trace element partition coefficients are important for using natural pyroxenes to estimate the compositions of the melts from which they crystallized and the oxidation conditions that prevailed during crystallization. We will report on minor element (Al, Ti, Cr) zoning in nakhlite pyroxenes and in synthetic pyroxenes that we have grown for the purposes of determining pyroxene/melt partition coefficients for Sr and REE. The natural pyroxenes have patchy Al zoning that, by analogy with our experimental pyroxenes, we interpret as sector zoning. The irregular patchy nature of the zoning is probably the result of the vagaries of growth kinetics and local environment during crystal growth. More slowly cooled nakhlites have the most distinct bimodal zoning, with one mode having Al2O3 around 0.5-0.6 wt%, and the other around 0.9 %. Average Al content increases with increasing cooling rate. This feature is puzzling, since the cumulus pyroxenes were almost certainly present at the time of eruption. Al and Ti are strongly correlated, but Cr is completely decoupled from those elements. The synthetic pyroxenes are distinctly sector zoned in Al and Ti, and the sector-to-sector variation in Al within a single crystal has important effects on trace element partition coefficients. Trivalent REE are strongly correlated with Al, while divalent elements (Sr, Eu+2) show a significantly weaker correlation. For example, as the Al2O3 content varies from 0.3 to 0.6 wt % from one sector to another, D(Gd) increases by approx.80% while D(Sr) and D(Eu) only increase by 20-30% at oxygen fugacities near IW. The different Al dependency of D for trivalent REE vs. divalent Eu and Sr considerably complicates the calibration of the Eu oxybarometer.

McKay, Gordon↗

NASA NTRS2006

Extension of DAMAS Phased Array Processing for Spatial Coherence Determination (DAMAS-C)

The present study reports a new development of the DAMAS microphone phased array processing methodology that allows the determination and separation of coherent and incoherent noise source distributions. In 2004, a Deconvolution Approach for the Mapping of Acoustic Sources (DAMAS) was developed which decoupled the array design and processing influence from the noise being measured, using a simple and robust algorithm. In 2005, three-dimensional applications of DAMAS were examined. DAMAS has been shown to render an unambiguous quantitative determination of acoustic source position and strength. However, an underlying premise of DAMAS, as well as that of classical array beamforming methodology, is that the noise regions under study are distributions of statistically independent sources. The present development, called DAMAS-C, extends the basic approach to include coherence definition between noise sources. The solutions incorporate cross-beamforming array measurements over the survey region. While the resulting inverse problem can be large and the iteration solution computationally demanding, it solves problems no other technique can approach. DAMAS-C is validated using noise source simulations and is applied to airframe flap noise test results.

Brooks, Thomas F.↗

NASA NTRS2006

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗

NASA NTRS2006

Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry

A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design variables such as the free stream parameters and the planform shape of an isolated wing. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Factors under consideration include the computation of mesh sensitivities that provide a reliable approximation of the objective function gradient, as well as the computation of surface shape sensitivities based on a direct-CAD interface. We present detailed gradient verification studies and then focus on a shape optimization problem for an Apollo-like reentry vehicle. The goal of the optimization is to enhance the lift-to-drag ratio of the capsule by modifying the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design.

Nemec, Marian↗