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DOE OSTI2026

Integrated geological, economic, and risk assessment of underground hydrogen storage

Underground hydrogen storage (UHS) is a promising option to buffer variable renewable power and support the hydrogen economy. Yet this technology is early-stage, and key uncertainties remain about how coupled processes such as geochemical and geomechanical impacts affect long-term storage security. In this paper, we seek to integrate the results from a large, multi-scale research program to quantify core feasibility metrics and situate these studies within ongoing efforts. Through this work, we evaluate hydrogen recoverability during storage by assessing diffusive losses, losses to geochemical interactions and their subsequent impact on geomechanical properties, and losses to residual saturation during injection and withdrawal. Molecular and laboratory studies show that lithologic heterogeneity, pore geometry, and mineral surface chemistry govern hydrogen–rock interactions, controlling loss pathways. High-pressure coreflooding is used to estimate relative permeabilities and measure parameters needed for reservoir-scale sensitivity analyses. These core-scale experiments found early hydrogen breakthrough at low saturations driven by capillary and viscous fingering, which limits pore-space utilization at early times, while repeated injection and withdrawal cycles improve deliverability over time. Technoeconomic factors and purity requirements for end uses are also considered as part of our comprehensive feasibility analysis. Finally, we underscore the importance of geophysical monitoring and tailored injection strategies to maintain integrity and efficiency. Together, these results provide a quantitative foundation for safe, scalable deployment of UHS and highlight priorities for future integrated studies.

08 HYDROGEN↗

DOE OSTI2020

Progress Report on Model Development for the Transport of Aerosol Through Microchannels

Accuracy of consequence assessments could be improved by accounting for the leak path deposition of aerosol in the source term. Recent experimental measurements from Sandia (2018) provided evidence of partial microchannel plugging due to particulate deposition. This filtration effect is relevant to the source term assessments and it is not unreasonable to anticipate that aerosol deposition in more realistic geometries could even lead to complete plugging of the leak path. This report summarizes current progress (as of end of Q3 FY 2020) on the development of a phenomenological model of aerosol transport, deposition, and plugging through microchannels. The purpose is to introduce a generic, reliable numerical model for the prediction of aerosol transport, deposition, and plugging in leak paths while accounting for potential plugging formation. This report includes (1) an overview of recent additions and improvements on the recently developed numerical model to analyze the various deposition processes in leak paths, to provide quantitative estimates of penetration factors, and to gain an understanding of the variables that affect them and (2) a summary of recent benchmarking results of the model’s validity with recent experimental measurements from Sandia.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1994

Modeling the bidirectional reflectance distribution function of mixed finite plant canopies and soil

An analytical model of the bidirectional reflectance for optically semi-infinite plant canopies has been extended to describe the reflectance of finite depth canopies contributions from the underlying soil. The model depends on 10 independent parameters describing vegetation and soil optical and structural properties. The model is inverted with a nonlinear minimization routine using directional reflectance data for lawn (leaf area index (LAI) is equal to 9.9), soybeans (LAI, 2.9) and simulated reflectance data (LAI, 1.0) from a numerical bidirectional reflectance distribution function (BRDF) model (Myneni et al., 1988). While the ten-parameter model results in relatively low rms differences for the BRDF, most of the retrieved parameters exhibit poor stability. The most stable parameter was the single-scattering albedo of the vegetation. Canopy albedo could be derived with an accuracy of less than 5% relative error in the visible and less than 1% in the near-infrared. Sensitivity were performed to determine which of the 10 parameters were most important and to assess the effects of Gaussian noise on the parameter retrievals. Out of the 10 parameters, three were identified which described most of the BRDF variability. At low LAI values the most influential parameters were the single-scattering albedos (both soil and vegetation) and LAI, while at higher LAI values (greater than 2.5) these shifted to the two scattering phase function parameters for vegetation and the single-scattering albedo of the vegetation. The three-parameter model, formed by fixing the seven least significant parameters, gave higher rms values but was less sensitive to noise in the BRDF than the full ten-parameter model. A full hemispherical reflectance data set for lawn was then interpolated to yield BRDF values corresponding to advanced very high resolution radiometer (AVHRR) scan geometries collected over a period of nine days. The resulting parameters and BRDFs are similar to those for the full sampling geometry, suggesting that the limited geometry of AVHRR measurements might be used to reliably retrieve BRDF and canopy albedo with this model.

Schluessel, G.↗

NASA NTRSDate not supplied

Design and Optimization of an Open Rotor Stage

Open rotor propulsors enable greatly increased effective bypass ratios over current aircraft engines, resulting in significantly improved efficiencies. One of the most promising of these geometries is the “open fan”, which consists of a single rotor followed by a single stator. This configuration will be referred to as an “open rotor stage” for design work at NASA. In this work we consider the multidisciplinary design and optimization of an open rotor stage using a variety of 2D and 3D techniques. The 2D aerodynamic techniques used for design include a 2D Trefftz plane method, axisymmetric throughflow, and quasi-3D blade-to-blade CFD. Aerodynamic performance is prioritized, while structural requirements are met and some acoustic considerations are included. Between the rotor, stator, and hub profiles, a total of 101 design variables are used. Differences in the process of designing an open rotor stage vs. designing other high-speed propellers are also discussed. The current design, the NASA Optimized Propulsor for Efficiency and Noise (N-OPEN-1), achieves 84.7% net efficiency as predicted by 3D CFD, with further improvements expected to be possible. This design makes effective use of a slower rotor and a less tip-loaded work distribution than typical single-rotation propellers, allowing the stator to produce 14.8% of the thrust. Laminar flow on the blades was responsible for a 1.7% efficiency benefit and warrants further study.

Open rotors↗

NASA NTRS2026

Design and Optimization of an Open Rotor Stage

turbomachinery↗

DOE OSTI2017

Statistical Analysis in Support of Control Fuel Temperature for the Advanced Gas Reactor Experiments

There are four completed tests among a series of Advanced Gas Reactor (AGR) irradiation experiments that are being conducted within the Advanced Reactor Technologies (ART) Fuel Development and Qualification Program. The main objectives of the fuel experimental campaigns are to provide the necessary data on fuel performance to support fuel process development, qualify a fuel design and fabrication process for normal operation and hypothetical accident conditions, and support development and validation of fuel performance and fission product transport models and codes.1 Since this tristructural isotropic fuel is qualified to be used in high temperature gas-cooled reactors (HTGRs), it is essential that the testing conditions of fuel irradiations are designed to mimic those in the conceptual gas reactors. As a result, temperatures of the AGR test fuel have to be maintained within a specified range that is typical of the HTGRs. In each AGR capsule, the test fuel temperature is controlled independently using a variable fraction neon and helium gas mixture that fills the gap volume for each capsule. The temperature as measured by a thermocouple (TC) terminated in the graphite holder (which houses fuel compacts) is used as a feedback for the gas flow controllers. Direct temperature measurement for fuel compacts is not possible because contact between a TC head and fuel particle could lead to undesirable failures. Therefore, an ABAQUS based finite element thermal model was created to predict the daily average fuel temperatures during the entire irradiation period.2,3 It is well-known that extended exposure to neutron irradiation and high temperatures leads to changes in geometries of fuel compacts and graphite holder, which result in changes of the gas gap leading to a change in the relationship between TC and fuel temperatures. In addition, TCs are also expected to drift and sometimes fail under irradiation conditions. These facts make maintaining test fuel temperature within a specified range challenging. This paper describes how the regression analysis methods are used in conjunction of calculated fuel temperatures from early irradiation periods (when irradiation effect is relatively small) to effectively control fuel temperature for the remaining irradiation, when irradiation effect became profound. This is particularly important in the event of all TCs in a capsule fail.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2017

Statistical Analysis in Support of Fuel Temperature Control in the Advanced Gas Reactor Experiments

There are four completed tests among a series of Advanced Gas Reactor (AGR) irradiation experiments that are being conducted within the Advanced Reactor Technologies (ART) Fuel Development and Qualification Program. The main objectives of the fuel experimental campaigns are to provide the necessary data on fuel performance to support fuel process development, qualify a fuel design and fabrication process for normal operation and hypothetical accident conditions, and support development and validation of fuel performance and fission product transport models and codes. Since this tri-structural isotropic fuel is qualified to be used in high temperature gas-cooled reactors (HTGRs), it is essential that the testing conditions of fuel irradiations are designed to mimic those in the conceptual gas reactors. As a result, temperatures of the AGR test fuel have to be maintained within a specified range that is typical of the HTGRs. In each AGR capsule, the test fuel temperature is controlled independently using a variable fraction neon and helium gas mixture that fills the gap volume for each capsule. The temperature as measured by a thermocouple (TC) terminated in the graphite holder (which houses fuel compacts) is used as a feedback for the gas flow controllers. Direct temperature measurement for fuel compacts is not possible because contact between a TC head and fuel particle could lead to undesirable failures. Therefore, an ABAQUS-based finite element thermal model was created to predict the daily average fuel temperatures during the entire irradiation period. It is well-known that extended exposure to neutron irradiation and high temperatures leads to changes in geometries of fuel compacts and graphite holder, which results in changes of the gas gap, leading to a change in the relationship between TC and fuel temperatures. In addition, TCs are expected to drift and sometimes fail under irradiation conditions. These facts make maintaining test fuel temperature within a specified range challenging. This paper describes how the regression analysis methods are used in conjunction with calculated fuel temperatures from early irradiation periods (when the irradiation effect is relatively small) to effectively control fuel temperature for the remaining irradiation (when the irradiation effect became profound). This is particularly important in the event when all TCs in a capsule fail.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Design and Characterization of an Extremely-Sensitive, Large-Volume Gamma-Ray Spectrometer for Environmental Samples

A large volume gamma spectrometer was designed and constructed to analyze foodstuffs and environmental samples having low radionuclide concentrations. This system uses eight 11-cm × 42.5-cm × 5.5-cm NaI(Tl) detectors, chosen due to their relatively high sensitivity and availability and arranged in an octagonal configuration. The sensitive volume of the system is ~28 cm in diameter and ~42 cm deep. Shielding consists of an 86-cm × 86-cm square, 64-cm-tall lead brick enclosure with 18-cm-thick lead walls lined by 0.3-cm-thick copper plates. An aluminum top was machined to suspend the detectors within this shield. The shielding reduces background counts by 72% at 100 keV and 42% at 1,000 keV. The positional variability in sensitivity of the well was determined by both simulation and experiment. A 2.1-L volume of nearly uniform sensitivity, varying less than 10%, exists in the well's center. Energy resolutions of 14.6% and 7.8% were measured for 241 Am and 137 Cs, respectively. Energy resolution shows a 0.2% variation for both 241 Am and 137 Cs as a function of position within all regions of the well’s central sensitive volume. Dead time was also determined to be less than 35% for all sources measured in the system, the largest of which had an activity of 1,760 kBq. Simulated results for various source geometries show higher counts for smaller samples, especially at lower energies due to less attenuation of low energy photons. In conclusion, minimum detectable activities were determined for all source energies used, less than 5.1 Bq kg -1 for reasonable background and sample counting times.

47 OTHER INSTRUMENTATION↗

NASA NTRS1984

Dynamics of early planetary gear trains

A method to analyze the static and dynamic loads in a planetary gear train was developed. A variable-variable mesh stiffness (VVMS) model was used to simulate the external and internal spur gear mesh behavior, and an equivalent conventional gear train concept was adapted for the dynamic studies. The analysis can be applied either involute or noninvolute spur gearing. By utilizing the equivalent gear train concept, the developed method may be extended for use for all types of epicyclic gearing. The method is incorporated into a computer program so that the static and dynamic behavior of individual components can be examined. Items considered in the analysis are: (1) static and dynamic load sharing among the planets; (2) floating or fixed Sun gear; (3) actual tooth geometry, including errors and modifications; (4) positioning errors of the planet gears; (5) torque variations due to noninvolute gear action. A mathematical model comprised of power source, load, and planetary transmission is used to determine the instantaneous loads to which the components are subjected. It considers fluctuating output torque, elastic behavior in the system, and loss of contact between gear teeth. The dynamic model has nine degrees of freedom resulting in a set of simultaneous second order differential equations with time varying coefficients, which are solved numerically. The computer program was used to determine the effect of manufacturing errors, damping and component stiffness, and transmitted load on dynamic behavior. It is indicated that this methodology offers the designer/analyst a comprehensive tool with which planetary drives may be quickly and effectively evaluated.

August, R.↗

DOE OSTI2020

Custom NEON AOP reflectance mosaics and maps of shade masks, canopy water content

This mosaic of visible to shortwave infrared (VSWIR) data was derived from the assignable asset NEON AOP radiance data that was collected by LBNL’s Watershed Function SFA during the summer of 2018 (DOI: 10.15485/1617204). This atmospheric correction was completed to take into account site-specific terrain variability in the 334 km2 survey area centered around Crested Butte, CO. The atmospheric correction was completed using ACORN atmospheric correction software executed on 200 x 200 pixel kernels rather than line by line in order to capture local flight altitude conditions. Manual cloud delineation removed any small shaded areas that occurred within the data collection areas. Mosaics were developed based on preference for days that were in close timing proximity to the coincident ground campaign and with mosaicing criteria that minimized the angle between the sun and the sensor to retrieve the most consistent reflectance (min_phase_refl_tiled). Finally, we generated shade masks based on the geometry between the sun angle at time of flight, the ground surface, and the sensor. Here we provide the orthomosaiced estimated reflectance data (min_phase_refl_tiled.tif), canopy water content (wtrl), estimated atmospheric water vapor (wtrv), the observational data (obs) for this particular mosaic, the estimated visibility (vis), shade masks derived from the digital surface elevation model (shade) and the digital terrain model (shade_tch) added to the canopy height model (DOI: 10.15485/1617203), and a wavelength metadata file. Each image file is provided as a GeoTiff with internal tiling and LZW compression. These data can also be found on Google Earth Engine for extraction, download, and analysis of smaller extents (Google Earth Engine data is linked in external link table).

2018 NEON and 2025 CHESS Campaigns↗

DOE OSTI2023

In-Situ Monitoring Assisted Large-Scale Additive Manufacturing of Mild Steel and 316L Alloys for Nuclear Application

The Advanced Materials and Manufacturing Technologies (AMMT) Program is aimed at developing cross-cutting technologies in support of a broad range of nuclear reactor parts, and to maintain U.S. leadership in materials and manufacturing technologies for nuclear energy applications. The overarching vision of the AMMT program is to accelerate the development, qualification, demonstration and deployment of advanced materials and manufacturing technologies to enable reliable and economical nuclear energy. One of its three goals is to target big challenges and game-changing technologies, to realize the mission and vision of AMMT program. Based on this context, this multi-year work package focuses on understanding the current state of large-scale additive manufacturing (AM) technology for the deposition of 316L stainless steel materials for final components and mild steel for use in nuclear manufacturing processes. The targeted AM modality is directed energy deposition (DED), capable of fabricating components on the size scale of meters including valves, pumps, impellers. etc. that are challenging or difficult to source, especially when developing new systems or replacing obsolete components. Accordingly, the current writeup aims at providing a baseline literature survey on structure-property relationships in mild steel and 316L alloys. Also, information on preliminary trials to date involving these two alloys show tremendous potential of printing parts having complex geometry and thin- walled structures, such as nuclear valve and Hot isostatic Press (HIP) can, using wire based (Wire Arc Additive Manufacturing and Hybrid Additive Manufacturing) as well as blown powder DED machines. All of this is aimed towards (i) demonstrating the ability to fabricate large components for pressure boundary applications relevant to the nuclear community and nuclear manufacturing technology, and (ii) understanding the effect of different manufacturing technology on AM can production and post HIPed material for nuclear applications. Another target of this writeup is to compile various in-situ monitoring tools that have been incorporated for different DED AM modalities, in order to understand process variability during the entire fabrication process. This can be correlated with processing-structure-property response surfaces and would add confidence around process quality verification and ultimately component certification for nuclear applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1985

Altimetry data and the elastic stress tensor of subduction zones

The stress field in the lithosphere caused by the distribution of density anomalies associated to the geoidal undulations observed by the GEOS-3 and SEASAT Earth satellites in the Tonga region was studied. Different models of the lithosphere were generated with different assumptions on the density distribution and geometry, all generating a geoid profile almost identical to the observed one. The first model is the Airy isostatic hypothesis which consists of a crust of density 2.85 laying on a lithosphere of density 3.35. The models obtained with different compensation depths give residual shortwavelength anomalies of the order of several tens of mgal and several tens of meters geoidal undulations. It indicates that there is no isostasy of the Airy type in the Tonga region because the observed geoid has very smooth undulation of about 25 m over a distance of 2000 km. The Pratt isostatic hypothesis is used in a model consisting of a crust of variable density laying on a lithosphere of higher density. This model gives smaller residual anomalies but still shows that there is no isostasy of the Pratt type in the Tonga region because the observed geoidal undulation are much smaller and smoother than the residual undulations associated to the Pratt model of isostasy.

Caputo, M.↗

NASA NTRS2000

Structure of the Circumnuclear Region of Seyfert 2 Galaxies Revealed by RXTE Hard X-Ray Observations of NGC 4945

NGC 4945 is one of the brightest Se.yfert galaxies on the sky at 100 keV, but is completely absorbed below 10 keV, implying an optical depth of the absorber to electron scattering of a few; its absorption column is probably the largest which still allows a direct view of the nucleus at hard X-ray energies. Our observations of it with the Rossi X-ray Timing Explorer (RXTE) satellite confirm the large absorption, which for a simple phenomenological fit using an absorber with Solar abundances implies a column of 4.5(sup 0.4, sub -0.4) x 10(exp 24) /sq cm. Using a a more realistic scenario (requiring Monte Carlo modeling of the scattering), we infer the optical depth to Thomson scattering of approximately 2.4. If such a scattering medium were to subtend a large solid angle from the nucleus, it should smear out any intrinsic hard X-ray variability on time scales shorter than the light travel time through it. The rapid (with a time scale of approximately a day) hard X-ray variability of NGC 4945 we observed with the RXTE implies that the bulk of the extreme absorption in this object does not originate in a parsec-size, geometrically thick molecular torus. Limits on the amount of scattered flux require that the optically thick material on parsec scales must be rather geometrically thin, subtending a half-angle < 10 deg. This is only marginally consistent with the recent determinations of the obscuring column in hard X-rays, where only a quarter of Seyfert 2s have columns which are optically thick, and presents a problem in accounting for the Cosmic X-ray Background primarily with AGN possessing the geometry as that inferred by us. The small solid angle of the obscuring material, together with the black hole mass (of approximately 1.4 x 10(exp 6) solar mass) from megamaser measurements. allows a robust determination of the source luminosity, which in turn implies that the source radiates at approximately 10% of the Eddington limit.

Madejski, G.↗

DOE OSTI2018

Extreme problem for partially nonoverlapping domains on a Riemann sphere

The results of this work are referred to the well-known trend of the geometric theory of functions of complex variable, namely, to the extreme problems on the classes of nonoverlapping domains. It was started by Lavrent’ev’s classical work [1], where, in particular, the problem of the product of conformal radii of two nonoverlapping domains was first solved. Now, this trend is intensively developed. The main results can be found in [2–8] and [9–13]. Our results present a generalization of some results in [7].

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Quantifying Reaction and Rate Heterogeneity in Battery Electrodes in 3D through Operando X-ray Diffraction Computed Tomography

In composite battery electrode architectures, local limitations in ionic and electronic transport can result in nonuniform energy storage reactions. Understanding such reaction heterogeneity is important to optimizing battery performance, including rate capability and mitigating degradation and failure. Here, we use spatially resolved X-ray diffraction computed tomography to map the reaction in a composite electrode based on the LiFePO 4 active material as it undergoes charge and discharge. Accelerated reactions at the electrode faces in contact with either the separator or the current collector demonstrate that both ionic and electronic transport limit the reaction progress. The data quantify how nonuniformity of the electrode reaction leads to variability in the charge/discharge rate, both as a function of time and position within the electrode architecture. Importantly, this local variation in the reaction rate means that the maximum rate that individual cathode particles experience can be substantially higher than the average, control charge/discharge rate, by a factor of at least 2-5 times. As a result, this rate heterogeneity may accelerate rate-dependent degradation pathways in regions of the composite electrode experiencing faster-than-average reaction and has important implications for understanding and optimizing rate-dependent battery performance. Benchmarking multiscale continuum model parameters against the observed reaction heterogeneity permits extension of these models to other electrode geometries.

25 ENERGY STORAGE↗

DOE OSTI2025

High-Pressure Effects on an Octa-Hydrated Curium Complex: An Experimental and Theoretical Investigation

An octa-hydrated curium compound [Cm(H 2 O) 8 ](Hdtp)(dtp)·H 2 O (Cm1,H 2 dtp = 2,3-di(tetrazol-5-yl)pyrazine) along with its lanthanide analogues [Ln(H 2 O) 8 ](Hdtp)-(dtp)·H 2 O (Ln1, Ln 3+ = La 3+ –Nd 3+ , Sm 3+ –Lu 3+ ) were synthesized and characterized using single crystal X-ray diffraction and spectroscopic methods. Bond length analysis of VIII Cm(III)–OH 2 (where VIII refers to the coordination number) was compared to VIII Ln(III)–OH 2 (Ln 3+ = Nd 3+ and Sm 3+ ), indicating similar VIII M(III)–OH 2 bond lengths owing to the similar eight-coordinate ionic radii of these VIII M(III) cations. Owing to the reduced coordination number, the VIII Cm(III)–OH 2 bond lengths were shorter than previously reported IX Cm(III)–OH 2 bonds in [Cm(H 2 O) 9 ](CF 3 SO 3 ) 3 . The octa-aquo complexes were also characterized by solid-state UV–vis–NIR spectroscopy in addition to variable-temperature and variable-pressure photoluminescence. Variable-pressure absorption spectra of Cm1 were compared with Ln1 and show that the Cm(III) f → f transitions have a stronger dependence on pressure than that observed in Ln1 (Ln 3+ = Nd 3+ and Sm 3+ ). The experimental and computational analyses reveal that the monotonic decrease in the computed energy difference between the ground state and the first excited state corresponds to the observed red shift of the photoluminescence peak. This is accompanied by a gradual reduction in the average Cm(III)–OH 2 bond length and a delocalization of spin densities, alongside an intensified interaction involving the 5f orbitals under increasing pressure. Furthermore, these changes accommodate the new geometry and collectively modify the energy landscape, resulting in peak broadening and quenching.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1987

Helicopter main-rotor speed effects on far-field acoustic levels

The design of a helicopter is based on an understanding of many parameters and their interactions. For example, in the design stage of a helicopter, the weight, engine, and rotor speed must be considered along with the rotor geometry when considering helicopter operations. However, the relationship between the noise radiated from the helicopter and these parameters is not well understood, with only limited model and full-scale test data to study. In general, these data have shown that reduced rotor speeds result in reduced far-field noise levels. This paper reviews the status of a recent helicopter noise research project designed to provide experimental flight data to be used to better understand helicopter rotor-speed effects on far-field acoustic levels. Preliminary results are presented relative to tests conducted with a McDonnell Douglas model 500E helicopter operating with the rotor speed as the control variable over the range of 103% of the main-rotor speed (NR) to 75% NR, and with the forward speed maintained at a constant value of 80 knots.

Mueller, Arnold W.↗

NASA NTRS1999

Ames Optimized TCA Configuration

Configuration design at Ames was carried out with the SYN87-SB (single block) Euler code using a 193 x 49 x 65 C-H grid. The Euler solver is coupled to the constrained (NPSOL) and the unconstrained (QNMDIF) optimization packages. Since the single block grid is able to model only wing-body configurations, the nacelle/diverter effects were included in the optimization process by SYN87's option to superimpose the nacelle/diverter interference pressures on the wing. These interference pressures were calculated using the AIRPLANE code. AIRPLANE is an Euler solver that uses a unstructured tetrahedral mesh and is capable of computations about arbitrary complete configurations. In addition, the buoyancy effects of the nacelle/diverters were also included in the design process by imposing the pressure field obtained during the design process onto the triangulated surfaces of the nacelle/diverter mesh generated by AIRPLANE. The interference pressures and nacelle buoyancy effects are added to the final forces after each flow field calculation. Full details of the (recently enhanced) ghost nacelle capability are given in a related talk. The pseudo nacelle corrections were greatly improved during this design cycle. During the Ref H and Cycle 1 design activities, the nacelles were only translated and pitched. In the cycle 2 design effort the nacelles can translate vertically, and pitch to accommodate the changes in the lower surface geometry. The diverter heights (between their leading and trailing edges) were modified during design as the shape of the lower wing changed, with the drag of the diverter changing accordingly. Both adjoint and finite difference gradients were used during optimization. The adjoint-based gradients were found to give good direction in the design space for configurations near the starting point, but as the design approached a minimum, the finite difference gradients were found to be more accurate. Use of finite difference gradients was limited by the CPU time limit available on the Cray machines. A typical optimization run using finite difference gradients can use only 30 to 40 design variables and one optimization iteration within the 8 hour queue limit for the chosen grid size and convergence level. The efficiency afforded by the adjoint method allowed for 50-120 design variables and 5-10 optimization iterations in the 8 hour queue. Geometric perturbations to the wing and fuselage were made using the Hicks/Henne (HH) shape functions. The HH functions were distributed uniformly along the chords of the wing defining sections and lofted linearly. During single-surface design, constraints on thickness and volume at selected wing stations were imposed. Both fuselage camber and cross-sectional area distributions were permitted to change during design. The major disadvantage to the use of these functions is the inherent surface waviness produced by repeated use of such functions. Many smoothing operations were required following optimization runs to produce a configuration with reasonable smoothness. Wagner functions were also used on the wing sections but were never used on the fuselage. The Wagner functions are a family of increasingly oscillatory functions that have also been used extensively in airfoil design. The leading and trailing edge regions of the wing were designed by use of polynomial and monomial functions respectively. Twist was attempted but was abandoned because of little performance improvement available from changing the baseline twist.

Cliff, Susan E.↗