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NASA NTRS2018

Predicting Global Ground Geoelectric Field With Coupled Geospace and Three-Dimensional Geomagnetic Induction Models

We forecast the global effects of space weather on the geoelectric and geomagnetic fields using a novel combination of methods. We use a realistic three-dimensional (3-D) model of Earth's electrical conductivity and a realistic representation of magnetospheric and ionospheric current systems. Our scheme involves the following steps: (1) We run a global magnetohydrodynamic model of the magnetosphere coupled to an electrostatic model of the ionosphere. (2) We calculate a global time series of the ground magnetic field resulting from the ionospheric, field-aligned, and magnetospheric currents of the global magnetohydrodynamic model. (3) We approximate this external field by an equivalent source current flowing in a thin shell above Earth. (4) We calculate a global time series of geoelectric and geomagnetic fields from the equivalent current and a 3-D conductivity model of Earth that also takes into account the coast effect due to large horizontal conductivity gradient. We verify our implementation by comparing the results against known analytic and numeric solutions, and then apply our scheme to the geomagnetic storm of 14 and 15 December 2006. In particular, we show that accounting for 3-D structure of Earth's conductivity results in significantly enhanced geoelectric field at large lateral gradients of conductivity, especially in coastal regions, both at middle and high latitudes. In the studied geomagnetic storm the largest values of 3-D geoelectric field are detected at high latitudes reaching 2.5 volts per kilometer and the 3-D effect extends inland by a few hundred kilometers.

Honkonen, I.↗

NASA NTRS1975

A two-level trajectory decomposition algorithm featuring optimal intermediate target selection

A decomposition algorithm is presented that optimizes complex missions by partitioning the trajectory into natural segments such as ascent or entry. Each segment defines a full-rank targeting subproblem. These are solved sequentially using the Newton-Raphson algorithm. The master problem, representing the complete mission, is to determine subproblem targets and master-problem controls that optimize the mission objective subject to intersegment constraints. The gradient projection algorithm solves this problem using derivatives obtained analytically from finite-difference subproblem sensitivities. Thus, the mission is optimized by coordinating the solution of tractible subproblems. Computational results for a synchronous equatorial mission are included.

Petersen, F. M.↗

NASA NTRS1976

Pressure and velocity in a developing coaxial jet

Determinations of static pressure, mean velocity and turbulence intensity in the developing region of coaxial jets are presented. Detailed profiles were obtained at twelve axial locations (extending from the nozzle exit for a distance of 5 diameters) downstream from a single element of the Bell Aerospace H2/O2 19-element coaxial injector. Measurements of mass-flux per unit area (using a constant temperature anemometer), total pressure and local temperature were used in the determination of local static pressure and velocity. These data show a low pressure region exists near the nozzle exit. Although this pressure reduction is small (0.34 psi), it substantially altered the flow development. Comparison of results shows that velocity near the nozzle exit decreases initially (no central velocity core) as a result of both pressure gradients and viscous mixing. These data are compared with analytical predictions made using available computer codes. Results show the need to consider pressure effects in any proposed mathematical model.

Moon, L. F.↗

NASA NTRS1977

A two-level trajectory decomposition algorithm featuring optimal intermediate target selection

A decomposition algorithm is presented which optimizes complex missions by partitioning the trajectory into natural segments such as ascent or entry. Each segment defines a full-rank targeting subproblem. These are solved sequentially using the Newton-Raphson algorithm. The master problem, representing the complete mission, is to determine subproblem targets and master-problem controls that optimize the mission objective subject to intersegment constraints. The gradient projection algorithm solves this problem using derivatives obtained analytically from finite-difference subproblem sensitivities. Thus, the mission is optimized by coordinating the solution of tractible subproblems. Computational results for a synchronous equatorial mission are included.

Petersen, F. M.↗

NASA NTRS1977

An information matrix approach for aircraft parameter-insensitive control

The Fisher Information Matrix provides the nucleus of a design procedure for obtaining parameter-insensitive feedback gains in Linear-Quadratic-Gaussian problems. The procedure minimizes a sum of performance and closed-loop sensitivity costs, the latter being related to the information content of the system response. Analytical expressions for the appended cost functional and its gradient with respect to the feedback gains are derived. These derivatives serve as the basis of a computationally efficient iterative algorithm that finds the optimal gains. Application of the technique is made to determine low sensitivity feedback gains for a C-5A wing loading alleviation system that has 15 states and three uncertain parameters.

Kleinman, D. L.↗

NASA NTRS1984

Convergent-tapered annular seals - Analysis and testing for rotordynamic coefficients

A combined analytical-computational method has been developed to calculate the pressure field and dynamic coefficients for tapered high-pressure annular seals. Completely developed turbulent flow is assumed in both the circumferential and axial directions, according to Hirs' (1973) bulk-flow turbulent-lubrication equations. In a numerical experiment with the method, a short bearing approximation is used to derive an analytical expression for the first-order (dynamic) pressure gradient. This expression is integrated numerically to define dynamic coefficients of the seal. Numerical results of the integration are compared with previous results for straight and tapered seals. It is found that direct stiffness and leakage coefficients increase in the present seal, while the remaining coefficients decrease. An optimal taper angle is shown to exist with respect to: (1) the direct stiffness and (2) the ratio of direct stiffness to leakage. On the basis of the optimal taper angle calculations, stiffness increases on the order of 40 to 50 percent are predicted. Experimental results for three taper angles are presented, and are found to be in good agreement with the theoretical predictions.

Childs, D. W.↗

NASA NTRS1990

Three-dimensional potential flows from functions of a 3D complex variable

Potential, or ideal, flow velocities can be found from the gradient of an harmonic function. An ordinary complex valued analytic function can be written as the sum of two real valued functions, both of which are harmonic. Thus, 2D complex valued functions serve as a source of functions that describe two-dimensional potential flows. However, this use of complex variables has been limited to two-dimensions. Recently, a new system of three-dimensional complex variables has been developed at the NASA Ames Research Center. As a step toward application of this theory to the analysis of 3D potential flow, several functions of a three-dimensional complex variable have been investigated. The results for two such functions, the 3D exponential and 3D logarithm, are presented in this paper. Potential flows found from these functions are investigated. Important characteristics of these flows fields are noted.

Kelly, Patrick↗

NASA NTRS2019

Load Flow Analysis with Analytic Derivatives for Electric Aircraft Design Optimization

Many of the aircraft concepts of the future are exploring the use of hybrid-, turbo- or all-electric propulsion systems to improve performance and decrease environmental impacts. These aircraft concepts range from small rotorcraft for urban air mobility to conventional commercial transports to large blended wing body designs. Developing the conceptual design for these vehicles presents a challenge, however, as traditional aircraft design tools often were not developed to handle these unique propulsion system architectures. Previous studies on these vehicles have therefore relied on relatively simple models of the electrical transmission and distribution system. This paper presents the development of a hybrid AC-DC load flow (or power flow) analysis capability to enhance the conceptual design of these concept vehicles. Specifically, the desire was to create a load flow analysis capability within the OpenMDAO framework that is also being used to develop a set of compatible tools for rapid optimization of conceptual designs. This load flow analysis capability is unique in its flexible object-oriented structure and implementation of analytic derivatives to facilitate the use of solvers and gradient based optimization in the design process. The developed hybrid load flow analysis capability is first verified against a published 13-bus example then used to model the electrical distribution system for a turbo-electric tiltwing aircraft.

Load flow↗

NASA NTRS1987

Structure, vibrational spectrum, and energetics of the CH5(+) ion - A theoretical investigation

Analytic derivative techniques are utilized to determine molecular geometries, vibration spectra, molecular force field, proton affinity, and energetics of clustering of protonated methane. It is observed that the geometries are gradient optimized, while the harmonic force fields and IR intensities are also determined analytically at the SCF level. It is determined that the frequency of the torsional model for rotation of the H2 about the pseudothreefold axis of the CH3(+) group is extremely low, and the proton affinity of CH4 is calculated as 129.0 kcal/mol.

Komornicki, Andrew↗

NASA NTRS2018

Real-Time Adaptive Drag Minimization Wind Tunnel Investigation of a Flexible Wing with Variable Camber Continuous Trailing Edge Flap System

This paper reports the results of a recently completed real-time adaptive drag minimization wind tunnel investigation of a highly flexible wing wind tunnel model equipped with the Variable Camber Continuous Trailing Flap (VCCTEF) technology at the University of Washington Aeronautical Laboratory (UWAL). The wind tunnel investigation is funded by NASA SBIR Phase II contract with Scientific Systems Company, Inc. (SSCI) and University of Washington (UW) as a subcontractor. The wind tunnel model is a sub-scale Common Research Model (CRM) wing constructed of foam core and fiberglass skin and is aeroelastically scaled to achieve a wing tip deflection of 10% of the wing semi-span which represents a typical wing tip deflection for a modern transport such as Boeing 787. The jig-shape twist of the CRM wing is optimized using a CART3D aero-structural model to achieve the minimum induced drag for the design cruise lift coefficient of 0.5. The wing is equipped with two chord wise cambered segments for each of the six span wise flap sections for a total of 12 individual flap segments that comprise the VCCTEF system. Each of the 12 flap segments is actively controlled by an electric servo-actuator. The real-time adaptive drag optimization strategy includes an on-board aerodynamic model identification, a model excitation, and a real-time drag optimization. The on-board aerodynamic model is constructed parametrically as a function of the angle of attack and flap positions to model the lift and drag coefficients of the wing. The lift coefficient models include a linear model and a second-order model. The drag coefficient models include a quadratic model and a higher-order up to 6th-order model to accurately model the drag coefficient at high angles of attack. The onboard aerodynamic model identification includes a recursive least-squares (RLS) algorithm and a batch least-squares (BLS) algorithm designed to estimate the model parameters. The model excitation method is designed to sample the input set that comprises the angle of attack and the flap positions. Three model excitation methods are developed: random excitation method, sweep method, and iterative angle-of-attack seeking method. The real-time drag optimization includes a generic algorithm developed by SSCI and several optimization methods developed by NASA which include a second-order gradient Newton-Raphson optimization method, an iterative gradient optimization method, a pseudo-inverse optimization method, an analytical optimization method, and an iterative refinement optimization method. The first wind tunnel test entry took place in September 2017. This test revealed major hardware issues and required further redesign of the flap servo mechanisms. The second test entry took place in April 2018. However, the test was not successful due to the issues with the onboard aerodynamic model identification RLS algorithm which incorrectly identified model parameters. This test also provides an experimental comparison study between the VCCTEF and a variable camber discrete trailing edge flap (VCDTEF) without the elastomer transition mechanisms. The experimental result confirms the benefit of the VCCTEF which produces lower drag by 5% than the VCDTEF. The third and final test entry took place in June 2018 after the issues with the RLS algorithm have been identified and corrected. Additional improvements were implemented. These include the BLS algorithm, the iterative angle-of-attack seeking method, the iterative gradient optimization method, and the pseudo-inverse optimization method. The test objectives were successfully demonstrated as the real-time drag optimization identifies several optimal solutions at off-design lift coefficients. The iterative gradient optimization method is found to achieve up to 4.7% drag reduction for the off-design lift coefficient of 0.7. The pseudo-inverse optimization method which does not require the drag coefficient model is found to be quite effective in reducing drag. Up to 9.4% drag reduction for the off-design lift coefficient of 0.7 is achieved with the pseudo-inverse optimization method. The wind tunnel investigation demonstrates the potential of real-time drag optimization technology. Several new capabilities are developed that could enable future adaptive wing technologies for flexible wings equipped with drag control devices such as the VCCTEF.

Drag Optimization↗

NASA NTRS1974

Supersonic laminar base pressure, heat-transfer, and upstream influence correlations for small steps

Some results of the application of a unified theory of small disturbances in nonuniform high-speed boundary layers to the small-step problem for the case of supersonic laminar nonadiabatic flow are described. Comparisons with experimental data are given which show good agreement in a variety of physical features, including useful new base pressure and heat-transfer correlation relations. Using a small perturbation approach, an analytical theory is developed that predicts the steady-state pressure, temperature, and heat-transfer disturbance fields including suction or blowing through the step. Particular emphasis is placed on the important effects of the highly nonuniform flow across the boundary layer, lateral pressure gradients, and the upstream influence associated with viscous-inviscid interaction. Approximate analytical expressions for the wall pressure, skin friction, and heat-transfer perturbations and upstream influence distance are derived by a Fourier transformation approach.

Inger, G. R.↗

NASA NTRS2016

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

A new engine cycle analysis tool, called Pycycle, was recently built using the OpenMDAO framework. This tool uses equilibrium chemistry based thermodynamics, and provides analytic derivatives. This allows for stable and efficient use of gradient-based optimization and sensitivity analysis methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a multi-point turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Turbine engine↗

NASA NTRS1995

Thermal barrier coating life modeling in aircraft gas turbine engines

Analytical models for predicting ceramic thermal barrier coating (TBC) spalling life in aircraft gas turbine engines are presented. Electron beam-physical vapor deposited (EB-PVD) and plasma sprayed TBC systems are discussed. An overview of the following TBC spalling mechanisms is presented: metal oxidation at the ceramic-metal interface, ceramic-metal interface stress singularities at edges and corners, ceramic-metal interface stresses caused by radius of curvature and interface roughness, material properties and mechanical behavior, temperature gradients, component design features and object impact damage. TBC spalling life analytical models are proposed based on observations of TBC spalling and plausible failure theories. TBC spalling was assumed to occur when the imposed stresses exceed the material strength (at or near the ceramic-metal interface). TBC failure knowledge gaps caused by lack of experimental evidence and analytical understanding are noted. The analytical models are considered initial engineering approaches that capture observed TBC failure trends.

Nissley, David M.↗

NASA NTRS2018

Contributions of Spherical Harmonics to Gravitational Moment

A scalar gravitational potential function expressed as a series of spherical harmonics frequently serves as the basis for a model of an astronomical body's gravitational field. The contribution of a generic spherical harmonic to gravitational gradient is expressed as a dyadic, which is then used to obtain an analytical expression in vector-dyadic form for the contribution to the moment of gravitational forces about the mass center of a small body such as a spacecraft. The expression developed for a harmonic's contribution to gravitational gradient can be applied in areas beyond the scope of the paper; for example, gravitational gradient plays an important role in the state propagation matrix and the state transition matrix that are used in spacecraft trajectory targeting and Kalman filtering. Additionally, it can be employed in numerical simulations of orbit determination based on measurements obtained with a gradiometer in low-Earth orbit. Contributions of spherical harmonics to gravitational moment may be of interest in connection with attitude control of a spacecraft in the vicinity of a body with an irregular shape, such as an asteroid. Normalized spherical harmonic coefficients up to degree and order 10 are obtained for the asteroid 216 Kleopatra and used in numerical evaluations of contributions to gravitational moment.

Roithmayr, Carlos M.↗

NASA NTRS1981

Voltage gradients in solar array cavities as possible breakdown sites in spacecraft-charging-induced discharges

A possible explanation for environmentally-induced discharges on geosynchronous satellites exists in the electric fields formed in the cavities between solar cells - the small gaps formed by the cover slides, solar cells, metallic interconnects and insulating substrate. When exposed to a substorm environment, the cover slides become less negatively charged than the spacecraft ground. If the resultant electric field becomes large enough, then the interconnect could emit electrons (probably by field emission) which could be accelerated to space by the positive voltage on the covers. An experimental study was conducted using a small solar array segment in which the interconnect potential was controlled by a power supply while the cover slides were irradiated by monoenergetic electrons. It was found that discharges could be triggered when the interconnect potential became at least 500 volts negative with respect to the cover slides. Analytical modeling of satellites exposed to substorm environments indicates that such gradients are possible. Therefore, it appears that this trigger mechanism for discharges is possible.

Stevens, N. J.↗

NASA NTRS1977

Prediction of Skylab attitude motion for space shuttle revisit

Computer simulations were employed to generate results, based on a fairly complicated analytical model. Environmental effects considered include atmospheric drag and gravity gradients. Mathematical models were based on Euler's moment equations and transformations from the body frame to inertial frame. A range of altitudes was considered, from 278 kilometers to 417 kilometers. Skylab is predicted to be in this orbital range during the 1979-1980 period. Results indicated that there will be a cyclic attitude motion due to the combined effect of gravity gradient and atmosphere drag. This motion can be characterized as being a slow tumble.

Alexander, S. G.↗

NASA NTRS1988

Optimization with artificial neural network systems - A mapping principle and a comparison to gradient based methods

General formulae for mapping optimization problems into systems of ordinary differential equations associated with artificial neural networks are presented. A comparison is made to optimization using gradient-search methods. The performance measure is the settling time from an initial state to a target state. A simple analytical example illustrates a situation where dynamical systems representing artificial neural network methods would settle faster than those representing gradient-search. Settling time was investigated for a more complicated optimization problem using computer simulations. The problem was a simplified version of a problem in medical imaging: determining loci of cerebral activity from electromagnetic measurements at the scalp. The simulations showed that gradient based systems typically settled 50 to 100 times faster than systems based on current neural network optimization methods.

Leong, Harrison Monfook↗

NASA NTRS2012

Surface, Water, and Air Biocharacterization (SWAB) Flight Experiment

The determination of risk from infectious disease during spaceflight missions is composed of several factors including both the concentration and characteristics of the microorganisms to which the crew are exposed. Thus, having a good understanding of the microbial ecology aboard spacecraft provides the necessary information to mitigate health risks to the crew. While preventive measures are taken to minimize the presence of pathogens on spacecraft, medically significant organisms have been isolated from both the Mir and International Space Station (ISS). Historically, the method for isolation and identification of microorganisms from spacecraft environmental samples depended upon their growth on culture media. Unfortunately, only a fraction of the organisms may grow on a specific culture medium, potentially omitting those microorganisms whose nutritional and physical requirements for growth are not met. To address this bias in our understanding of the ISS environment, the Surface, Water, and Air Biocharacterization (SWAB) Flight Experiment was designed to investigate and develop monitoring technology to provide better microbial characterization. For the SWAB flight experiment, we hypothesized that environmental analysis using non-culture-based technologies would reveal microorganisms, allergens, and microbial toxins not previously reported in spacecraft, allowing for a more complete health assessment. Key findings during this experiment included: a) Generally, advanced molecular techniques were able to reveal a few organisms not recovered using culture-based methods; however, there is no indication that current monitoring is "missing" any medically significant bacteria or fungi. b) Molecular techniques have tremendous potential for microbial monitoring, however, sample preparation and data analysis present challenges for spaceflight hardware. c) Analytical results indicate that some molecular techniques, such as denaturing gradient gel electrophoresis (DGGE), can be much less sensitive than culture-based methods. d) More sensitive molecular techniques, such as quantitative polymerase chain reaction (QPCR), were able to identify viral DNA from ISS environments, suggesting potential transfer of the organism between crewmembers. In addition, the hardware selected for this experiment represented advances for next-generation sample collection. The advanced nature of this collection hardware was noted, when the Sartorius MD8 Air Port air sampler from the SWAB experiment remained on board ISS at the request of JAXA investigators, who intend to use it in completion of their microbial ecology experiment.

Castro, V. A.↗