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NASA NTRS1980

Numerical calculation of steady inviscid full potential compressible flow about wind turbine blades

An exact nonlinear mathematical model that accounts for three-dimensional cascade effects about the inner portions of the rotor blades and compressibility effects about the tip regions of the blades was derived. An artificially time dependent version was iteratively solved by a finite volume technique involving an artificial viscosity and a three-level consecutive mesh refinement. The exact boundary conditions were applied by generating a boundary conforming periodic computation mesh.

Dulikravich, D. S.↗

NASA NTRS1980

Numerical calculation of steady inviscid full potential compressible flow about wind turbine blades

The air flow through a propeller-type wind turbine rotor is characterized by three-dimensional rotating cascade effects about the inner portions of the rotor blades and compressibility effects about the tip regions of the blades. In the case of large rotor diameter and/or increased rotor angular speed, the existence of small supersonic zones terminated by weak shocks is possible. An exact nonlinear mathematical model (called a steady Full Potential Equation - FPE) that accounts for the above phenomena has been rederived. An artificially time dependent version of FPE was iteratively solved by a finite volume technique involving an artificial viscosity and a three-level consecutive mesh refinement. The exact boundary conditions were applied by generating a boundary conforming periodic computation mesh.

Dulikravich, D. S.↗

NASA NTRS2015

Automated Point Cloud Correspondence Detection for Underwater Mapping Using AUVs

An algorithm for automating correspondence detection between point clouds composed of multibeam sonar data is presented. This allows accurate initialization for point cloud alignment techniques even in cases where accurate inertial navigation is not available, such as iceberg profiling or vehicles with low-grade inertial navigation systems. Techniques from computer vision literature are used to extract, label, and match keypoints between "pseudo-images" generated from these point clouds. Image matches are refined using RANSAC and information about the vehicle trajectory. The resulting correspondences can be used to initialize an iterative closest point (ICP) registration algorithm to estimate accumulated navigation error and aid in the creation of accurate, self-consistent maps. The results presented use multibeam sonar data obtained from multiple overlapping passes of an underwater canyon in Monterey Bay, California. Using strict matching criteria, the method detects 23 between-swath correspondence events in a set of 155 pseudo-images with zero false positives. Using less conservative matching criteria doubles the number of matches but introduces several false positive matches as well. Heuristics based on known vehicle trajectory information are used to eliminate these.

Sonar↗

NASA NTRSDate not supplied

System Modeling of a Lunar Molten Regolith Electrolysis Plant

Introduction: In-Situ Resource Utilization (ISRU) is the process of extracting local resources to produce commodities for propulsion, life support systems, and off-planet construction rather than transporting consumables from Earth. Molten Regolith Electrolysis (MRE) is a novel ISRU method of extracting oxygen gas and metal alloy from lunar regolith. The MRE process involves placing lunar regolith between two electrodes, through which current is passed, to melt the regolith and reduce the metal oxide constituents by direct electrolysis (e.g. FeO, SiO2, MgO, Al2O3) into oxygen gas and metal alloys. The oxygen is liquefied and used as propellant for landers, while the metals (e.g. Ferro-alloys) are further processed and used in structural building materials and parts manufacturing. A system model was developed that accounted for the major processes of an MRE plant (from excavation of raw materials to storage of products) to assess the feasibility of a lunar MRE plant. The System Engineering and Integration (SE&I) ISRU Modeling and Analysis (SIMA) team utilized its previously documented system sizing model, the Mission Analysis and Integration Tool (MAIT) [1] as framework of the system model. MAIT uses MATLAB/Simulink to integrate subsystem models into a complete system model of the MRE plant. Total mass, volume, and power requirements were computed for numerous iterations of a MRE plant. System Model: Figure 1: MRE Plant Block Diagram The regolith excavation model determines the mass and power needed to excavate sufficient regolith. The preheating auger initiates the regolith heating process before regolith enters the MRE re-actor to reduce the energy required to turn the solid into a molten liquid. The MRE reactor is modeled in COMSOL Multiphysics and based on the research by Dominguez, Sibille, and Schreiner [2, 3, 4]. This preliminary reactor model provides an accurate calculation of thermal equilibrium during electrochemical operation of the reactor system to assess the optimal mass and power required to process the inlet flow of regolith. The model also computes the outlet flowrates of oxygen and molten products. For this analysis, the primary components of the metal alloy considered were iron and silicon. The oxygen is then purified using an Yttrium Stabilized Zirconia (YSZ) electrode, followed by liquefaction using a 90K cryocooler to be stored as liquid oxygen in insulated cylindrical tanks. In future iterations of the system model, the molten metal tapped from the MRE reactor will undergo additional processing or refinement. However, downstream handling of metals is currently a technology gap that is missing a high TRL subsystem model. Therefore, for this analysis, the accumulated metal alloy stream terminates after leaving the MRE reactor. Study Goals: This analysis investigates multiple input variables to the system to determine the sensitivity of a (near) complete plant at full-scale. This preliminary investigation ran parametric sweeps on the MRE reactor geometry, electrical current supply, layers of multi-layer insulation (MLI) on the reactor, size of the electrodes in the oxygen purification model, and regolith composition (based on landing site location). Three production targets of oxygen (1,000, 10,000, and 50,000 kg/yr) were investigated for this analysis. The parametric sweeps conducted in this analysis provide valuable insight into the expected impact of the various model inputs on plant size. This information can be used to identify the most critical components of the plant and guide future decisions on allocating funding for research and development, providing subsystem developers with appropriate interfaces with downstream and upstream processes, and assessing the overall feasibility of MRE when compared to other ISRU plants. References: [1] Carlson, A. et al. (2024) ICES, ICES-2024-53. [2] Dominguez, D.A., and Sibille, L. (2011) AIAA, AIAA-2011-700. [3] Schreiner, S.S. (2015) MIT, Dissertation. [4] Schreiner, S.S. et al. (2016) ASR, 57(7), pp.1585-1603.

ISRU↗

NASA NTRSDate not supplied

Metallic Powder Core Tubular Wire (PCTW) Development for Additive Manufacturing

NASA Langley Research Center (LaRC) in Hampton, VA, and the Center for Welding, Joining, and Coating Research (CWJCR) in the Department of Metallurgical and Materials Engineering at the Colorado School of Mines (CSM) in Golden, CO, have collaborated for nearly fifteen years to develop metallic powder core tubular wire (PCTW) feedstock for additive manufacturing (AM) using electron beam deposition. The motivation for this development was to offset dealloying observed during deposition of titanium and aluminum alloy solid wire feedstock in the LaRC electron beam freeform fabrication (EBF3) system and to explore novel alloy compositions by tailoring the powder fill. EBF3 is a fusion-based AM process that is performed under vacuum and is consequently prone to vaporization loss of low vapor pressure alloying elements. Research spanning four graduate student research projects succeeded in developing the basic methodology to fabricate PCTW, the mass balance equations used to define the powder fill, microstructure control through particulate inoculation, and the feasibility of producing metal matrix composite materials. Metallic PCTW is comprised of a thin foil sheath wrapped around a powder blend. Fabrication of PCTW at CSM was accomplished using a tubular wire mill system to first bend a flat strip into a u-shaped cross section, deposit a powder fill, create a lap joint to seal the wire, and draw to final diameter. Powder management systems were developed to ensure uniform mixing of powder constituents and identify feed rates for optimum fill ratios. Processing parameters were successfully developed for titanium and aluminum alloy sheaths to account for material work hardening during drawing. Mass balance equations were developed to account for compositional contributions of the sheath and powder fill. PCTW composition can be adjusted through selection of the sheath or powder materials. PCTWs were successfully developed to offset Al loss in deposits of Ti-6-4 and Mg loss in Al 6061, resulting in deposits that were within the composition limits for each material. Ti-6-4 deposits were fabricated using PCTW comprised of commercially pure (CP) titanium sheath and a fill of pre-alloyed Ti-6-4 powder with additions of elemental Al and V powders. Additions of both elements were required to account for the CP Ti from the sheath, and Al was further enhanced to offset documented losses in EBF3 deposits. For Al 6061 deposits, composition was modulated through the choice of sheath material. The PCTW was made using an Al 5052 sheath to supplement Mg content and a fill composition of pre-alloyed 6061 powder with additions of Si and Cu.The slower solidification rate of the EBF3 process compared with laser powder bed fusion processes can lead to coarse-grained microstructures and mechanical property anisotropy. EBF3deposits of Ti-6-4 exhibited large epitaxially grown β grains, which result in degraded mechanical properties in the deposition direction. Microstructure refinement was achieved through a combination of electron beam modulation and the use of a PCTW designed for Ti-6-4 deposits and modified by the addition of powder made from Fe and B. Resulting deposits exhibited reductions in β grain size, α phase colony intercept length and lath width, and an increased volume fraction of β phase. The mechanism of microstructure refinement was related to precipitation of boride particles. Hardness testing confirmed that mechanical property anisotropy was reduced and an overall increase in hardness was achieved.Metal matrix composite (MMC) materials offer strength and stiffness benefits over unreinforced materials. Two methods were investigated using PCTW technology for producing Al 6061 basedMMC materials; the direct addition of SiC reinforcing particles and the in-situ generation of reinforcements through reaction synthesis of precursor powders. Al 6061 based MMCs reinforced with SiC exhibited particle clustering and formation of aluminum carbides during deposition. The application of a Ni coating to the SiC particles prior to incorporation into the powder fill eliminated aluminum carbide formation and aided particle distribution during deposition. Modulation of beam focus and power further reduced aluminum carbide formation and aided particle distribution. In reaction synthesis, precursor additions undergo an exothermic reaction during deposition to form new ceramic products, generally of finer scale than the initial precursor components. The product phases provide reinforcement in the MMC and act as nucleation sites during solidification, resulting in grain refinement, improved mechanical properties, and reduced susceptibility to solidification cracking. Higher tensile strength and stiffness were demonstrated in Al 6061 based MMCs with 2 vol% reinforcement. These combined research efforts demonstrate the potential of PCTW technology for customizing of alloy composition and achieving microstructure control. A manufacturing process for titanium- and aluminum-based PCTWs was developed based on iterative design, theoretical calculations, and empirical data. PCTW technology successfully mitigated Al loss from Ti-6-4 and Mg loss in Al 6061, resulted in grain refinement in Ti-6-4, and demonstrated fabrication of Al based MMCs

Marcia S Domack↗

NASA NTRS2005

Combined Radar and Radiometer Analysis of Precipitation Profiles for a Parametric Retrieval Algorithm

A methodology to analyze precipitation profiles using the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and precipitation radar (PR) is proposed. Rainfall profiles are retrieved from PR measurements, defined as the best-fit solution selected from precalculated profiles by cloud-resolving models (CRMs), under explicitly defined assumptions of drop size distribution (DSD) and ice hydrometeor models. The PR path-integrated attenuation (PIA), where available, is further used to adjust DSD in a manner that is similar to the PR operational algorithm. Combined with the TMI-retrieved nonraining geophysical parameters, the three-dimensional structure of the geophysical parameters is obtained across the satellite-observed domains. Microwave brightness temperatures are then computed for a comparison with TMI observations to examine if the radar-retrieved rainfall is consistent in the radiometric measurement space. The inconsistency in microwave brightness temperatures is reduced by iterating the retrieval procedure with updated assumptions of the DSD and ice-density models. The proposed methodology is expected to refine the a priori rain profile database and error models for use by parametric passive microwave algorithms, aimed at the Global Precipitation Measurement (GPM) mission, as well as a future TRMM algorithms.

Masunaga, Hirohiko↗

NASA NTRS2014

Explaining Earths Energy Budget: CERES-Based NASA Resources for K-12 Education and Public Outreach

Among atmospheric scientists, the importance of the Earth radiation budget concept is well understood. Papers have addressed the topic for over 100 years, and the large Clouds and the Earth's Radiant Energy System (CERES) science team (among others), with its multiple on-orbit instruments, is working hard to quantify the details of its various parts. In education, Earth's energy budget is a concept that generally appears in middle school and Earth science curricula, but its treatment in textbooks leaves much to be desired. Students and the public hold many misconceptions, and very few people have an appreciation for the importance of this energy balance to the conditions on Earth. More importantly, few have a correct mental model that allows them to make predictions and understand the effect of changes such as increasing greenhouse gas concentrations. As an outreach element of the core CERES team at NASA Langley, a multi-disciplinary group of scientists, educators, graphic artists, writers, and web developers has been developing and refining graphics and resources to explain the Earth's Energy budget over the last few decades. Resources have developed through an iterative process involving ongoing use in front of a variety of audiences, including students and teachers from 3rd to 12th grade as well as public audiences.

Chambers, L. H.↗

NASA NTRS2004

Processing of High Resolution, Multiparametric Radar Data for the Airborne Dual-Frequency Precipitation Radar APR-2

Following the successful Precipitation Radar (PR) of the Tropical Rainfall Measuring Mission, a new airborne, 14/35 GHz rain profiling radar, known as Airborne Precipitation Radar - 2 (APR-2), has been developed as a prototype for an advanced, dual-frequency spaceborne radar for a future spaceborne precipitation measurement mission. . This airborne instrument is capable of making simultaneous measurements of rainfall parameters, including co-pol and cross-pol rain reflectivities and vertical Doppler velocities, at 14 and 35 GHz. furthermore, it also features several advanced technologies for performance improvement, including real-time data processing, low-sidelobe dual-frequency pulse compression, and dual-frequency scanning antenna. Since August 2001, APR-2 has been deployed on the NASA P3 and DC8 aircrafts in four experiments including CAMEX-4 and the Wakasa Bay Experiment. Raw radar data are first processed to obtain reflectivity, LDR (linear depolarization ratio), and Doppler velocity measurements. The dataset is then processed iteratively to accurately estimate the true aircraft navigation parameters and to classify the surface return. These intermediate products are then used to refine reflectivity and LDR calibrations (by analyzing clear air ocean surface returns), and to correct Doppler measurements for the aircraft motion. Finally, the the melting layer of precipitation is detected and its boundaries and characteristics are identifIed at the APR-2 range resolution of 30m. The resulting 3D dataset will be used for validation of other airborne and spaceborne instruments, development of multiparametric rain/snow retrieval algorithms and melting layer characterization and statistics.

airborne radar↗

NASA NTRS1982

Profiles of electrified drops and bubbles

Axisymmetric equilibrium shapes of conducting drops and bubbles, (1) pendant or sessile on one face of a circular parallel-plate capacitor or (2) free and surface-charged, are found by solving simultaneously the free boundary problem consisting of the augmented Young-Laplace equation for surface shape and the Laplace equation for electrostatic field, given the surface potential. The problem is nonlinear and the method is a finite element algorithm employing Newton iteration, a modified frontal solver, and triangular as well as quadrilateral tessellations of the domain exterior to the drop in order to facilitate refined analysis of sharply curved drop tips seen in experiments. The stability limit predicted by this computer-aided theoretical analysis agrees well with experiments.

Basaran, O. A.↗

NASA NTRS1989

Prediction of turbine rotor-stator interaction using Navier-Stokes methods

Flows in turbomachinery are generally complex and do not easily lend themselves to numerical computation. The flows are three-dimensional and inherently unsteady. Complicated blade geometries and flow phenomena such as separation and periodic transition from laminar to turbulent flow add to the numerical complexity. Nevertheless, the accurate numerical analysis of such flows is a problem of considerable interest and practical importance to the turbomachinery community. Much of the early work in turbomachinery flow prediction focussed on airfoil cascades. While such analyses of flows in isolated airfoil rows have helped improve understanding of the flow phenomena and have gained widespread acceptance in the industrial community as a design tool, they do not yield any information regarding the unsteady effects arising out of rotor-stator aerodynamic interaction. These interaction effects become increasingly important as the distance between successive stator and rotor rows is decreased. Thus, the need exists for analytical tools that treat the rotor and stator airfoils as a system and provide information regarding the magnitude and the impact of the unsteady effects. The focus a three-dimensional, time-accurate, thin-layer Navier-Stokes code that was recently developed to study rotor-stator interaction problems. A system of patched and overlaid grids that move relative to each other is used to discretize the flow field and the governing equations are integrated using a third-order upwind scheme set in an iterative, implicit framework. The code was used to simulate subsonic flow through an axial turbine configuration for which considerable experimental data exists. Grid refinement studies were also conducted as part of the code validation process. The current status of the research, along with planned future directions, are also discussed.

Madavan, Nateri K.↗

NASA NTRS2017

CisLunar Habitat Internal Architecture Design Criteria

BACKGROUND: In preparation for human exploration to Mars, there is a need to define the development and test program that will validate deep space operations and systems. In that context, a Proving Grounds CisLunar habitat spacecraft is being defined as the next step towards this goal. This spacecraft will operate differently from the ISS or other spacecraft in human history. The performance envelope of this spacecraft (mass, volume, power, specifications, etc.) is being defined by the Future Capabilities Study Team. This team has recognized the need for a human-centered approach for the internal architecture of this spacecraft and has commissioned a CisLunar Phase-1 Habitat Internal Architecture Study Team to develop a NASA reference configuration, providing the Agency with a "smart buyer" approach for future acquisition. THE CISLUNAR HABITAT INTERNAL ARCHITECTURE STUDY: Overall, the CisLunar Habitat Internal Architecture study will address the most significant questions and risks in the current CisLunar architecture, habitation, and operations concept development. This effort is achieved through definition of design criteria, evaluation criteria and process, design of the CisLunar Habitat Phase-1 internal architecture, and the development and fabrication of internal architecture concepts combined with rigorous and methodical Human-in-the-Loop (HITL) evaluations and testing of the conceptual innovations in a controlled test environment. The vision of the CisLunar Habitat Internal Architecture Study is to design, build, and test a CisLunar Phase-1 Habitat Internal Architecture that will be used for habitation (e.g. habitability and human factors) evaluations. The evaluations will mature CisLunar habitat evaluation tools, guidelines, and standards, and will interface with other projects such as the Advanced Exploration Systems (AES) Program integrated Power, Avionics, Software (iPAS), and Logistics for integrated human-in-the-loop testing. The mission of the CisLunar Habitat Internal Architecture Study is to become a forcing function to establish a common understanding of CisLunar Phase-1 Habitation Internal Architecture design criteria, processes, and tools. The scope of the CisLunar Habitat Internal Architecture study is to design, develop, demonstrate, and evaluate a Phase-1 CisLunar Habitat common module internal architecture based on design criteria agreed to by NASA, the International Partners, and Commercial Exploration teams. This task is to define the CisLunar Phase-1 Internal Architecture Government Reference Design, assist NASA in becoming a "smart buyer" for Phase-1 Habitat Concepts, and ultimately to derive standards and requirements from the Internal Architecture Design Process. The first step was to define a Habitat Internal Architecture Design Criteria and create a structured philosophy to be used by design teams as a filter by which critical aspects of consideration would be identified for the purpose of organizing and utilizing interior spaces. With design criteria in place, the team will develop a series of iterative internal architecture concept designs which will be assessed by means of an evaluation criteria and process. These assessments will successively drive and refine the design, leading to the combination and down-selection of design concepts. A single refined reference design configuration will be developed into in a medium-to-high fidelity mockup. A multi-day human-in-the-loop mission test will fully evaluate the reference design and validate its configuration. Lessons learned from the design and evaluation will enable the team to identify appropriate standards for Phase-1 CisLunar Habitat Internal Architecture and will enable NASA to develop derived requirements in support of maturing CisLunar Habitation capabilities. This paper will describe the criteria definition process, workshop event, and resulting CisLunar Phase-1 Habitat Internal Architecture Design Criteria.

Jones, R.↗

NASA NTRS1990

A hybrid method for prediction of propeller performance

An analytical/computational code has been developed to predict the performance of advanced turboprop propellers. The method of solution is based on strip theory and conservation of linear and angular momenta applied to a control volume enclosing the propeller and its far wake. An iterative procedure is used to account for the induced axial and rotational velocities. Sectional aerodynamic coefficients are explicitly accounted for by thin airfoil theory and refinement of the results is obtained using a two-dimensional vortex panel method and Euler equations. The results obtained compare well with wind-tunnel data obtained for advanced propellers, such as the Hamilton Standard SR-2 and SR-7.

Takallu, M. A.↗

NASA NTRS2006

A Description of the "Crow's Foot" Tunnel Concept

NASA Langley Research Center has actively pursued the development and the use of pictorial or three-dimensional perspective displays of tunnel-, pathway- or highway-in-the-sky concepts for presenting flight path information to pilots in all aircraft categories (e.g., transports, General Aviation, rotorcraft) since the late 1970s. Prominent among these efforts has been the development of the crow s foot tunnel concept. The crow's foot tunnel concept emerged as the consensus pathway concept from a series of interactive workshops that brought together government and industry display designers, test pilots, and airline pilots to iteratively design, debate, and fly various pathway concepts. Over years of use in many simulation and flight test activities at NASA and elsewhere, modifications have refined and adapted the tunnel concept for different applications and aircraft categories (i.e., conventional transports, High Speed Civil Transport, General Aviation). A description of those refinements follows the definition of the original tunnel concept.

Parrish, Russell V.↗

NASA NTRS2024

Starling Formation-Flying Optical Experiment: Initial Operations and Flight Results

This paper presents initial flight results for angles-only navigation of a swarm of small spacecraft, conducted during the Starling Formation-Flying Optical Experiment (StarFOX). StarFOX is one of four experiments aboard the NASA Starling mission, which consists of four CubeSats launched in July 2023. Angles-only methods apply inter-satellite bearing angles obtained by on-board cameras for navigation, increasing satellite autonomy and enabling new mission concepts. Nevertheless, prior flight demonstrations have only featured one observer and target and have relied upon a-priori target orbit knowledge for initialization, translational maneuvers to resolve target range, and external absolute orbit updates to maintain convergence. StarFOX overcomes these limitations by applying the angles-only Absolute and Relative Trajectory Measurement System (ARTMS), which integrates three novel algorithms. Image Processing detects and tracks multiple targets in images, using multi-hypothesis methods and domain-specific kinematic modeling, and computes target bearing angles. Batch Orbit Determination computes initial swarm orbit estimates from bearing angle batches, via iterative batch least squares and sampling of the weakly observable target range. Sequential Orbit Determination leverages an adaptive, efficient unscented Kalman filter with nonlinear models to refine swarm state estimates over time. Multi-observer measurements shared over an intersatellite link are seamlessly fused to enable robust absolute and relative orbit determination. Initial StarFOX experiments are the first demonstrations of autonomous angles-only navigation for a satellite swarm, including multi-target and multi-observer relative navigation; autonomous initialization of navigation for unknown targets; and simultaneous absolute and relative orbit determination. Relative navigation accuracy of 1% (single observer) and 0.2% (multi-observer) of the inter-satellite range is achieved under challenging measurement conditions. Results demonstrate promising performance with regards to ongoing StarFOX campaigns and the application of angles-only navigation to future distributed missions.

Relative Navigation↗

NASA NTRS2016

Assessment of Preconditioner for a USM3D Hierarchical Adaptive Nonlinear Method (HANIM) (Invited)

Enhancements to the previously reported mixed-element USM3D Hierarchical Adaptive Nonlinear Iteration Method (HANIM) framework have been made to further improve robustness, efficiency, and accuracy of computational fluid dynamic simulations. The key enhancements include a multi-color line-implicit preconditioner, a discretely consistent symmetry boundary condition, and a line-mapping method for the turbulence source term discretization. The USM3D iterative convergence for the turbulent flows is assessed on four configurations. The configurations include a two-dimensional (2D) bump-in-channel, the 2D NACA 0012 airfoil, a three-dimensional (3D) bump-in-channel, and a 3D hemisphere cylinder. The Reynolds Averaged Navier Stokes (RANS) solutions have been obtained using a Spalart-Allmaras turbulence model and families of uniformly refined nested grids. Two types of HANIM solutions using line- and point-implicit preconditioners have been computed. Additional solutions using the point-implicit preconditioner alone (PA) method that broadly represents the baseline solver technology have also been computed. The line-implicit HANIM shows superior iterative convergence in most cases with progressively increasing benefits on finer grids.

Pandya, Mohagna J.↗

NASA NTRS1981

Accuracy and convergence of a finite element algorithm for turbulent boundary layer flow

The Galerkin-Weighted Residuals formulation is employed to derive an implicit finite element solution algorithm for the nonlinear parabolic partial differential equation system governing turbulent boundary layer flow. Solution accuracy and convergence with discretization refinement are quantized in several error norms using linear and quadratic basis functions. Richardson extrapolation is used to isolate integration truncation error in all norms, and Newton iteration is employed for all equation solutions performed in double-precision. The mathematical theory supporting accuracy and convergence concepts for linear elliptic equations appears extensible to the nonlinear equations characteristic of turbulent boundary layer flow.

Soliman, M. O.↗

NASA NTRS1982

Comparison of starting values for iterative solutions to a universal Kepler's equation

General starting values for the iterative numerical solution of a universal Kepler's equation for position in a conic orbit at a specified time are investigated. Three starting values based on recent refinements of previously obtained bounds on the solution are derived and tested numerically. Of these, a simple starting value based on a cubic approximation to Kepler's equation provides the most rapid convergence using both first and second order Newton algorithms. The performance of the starting values are compared with similar studies which used the restricted case of elliptical orbits with the initial epoch at periapse.

Bergam, M. J.↗

NASA NTRS2010

A Mixed-Fidelity Approach for Design of Low-Boom Supersonic Aircraft

This paper documents a mixed-fidelity approach for the design of low-boom supersonic aircraft as a viable approach for designing a practical low-boom supersonic configuration. A low-boom configuration that is based on low-fidelity analysis is used as the baseline. Tail lift is included to help tailor the aft portion of the ground signature. A comparison of low- and high-fidelity analysis results demonstrates the necessity of using computational fluid dynamics (CFD) analysis in a low-boom supersonic configuration design process. The fuselage shape is modified iteratively to obtain a configuration with a CFD equivalent-area distribution that matches a predetermined low-boom target distribution. The mixed-fidelity approach can easily refine the low-fidelity low-boom baseline into a low-boom configuration with the use of CFD equivalent-area analysis. The ground signature of the final configuration is calculated by using a state-of-the-art CFD-based boom analysis method that generates accurate midfield pressure distributions for propagation to the ground with ray tracing. The ground signature that is propagated from a midfield pressure distribution has a shaped ramp front, which is similar to the ground signature that is propagated from the CFD equivalent-area distribution. This result confirms the validity of the low-boom supersonic configuration design by matching a low-boom equivalent-area target, which is easier to accomplish than matching a low-boom midfield pressure target.

Li, Wu↗