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Results for “Analytic linearization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6

Impact of airfoil profile on the supersonic aerodynamics of delta wings

A nonlinear flow model was employed to predict the flowfield, pressure and force data for delta wings at supersonic speeds. The goal of the study was to investigate the influence the airfoil profiles has on the wing aerodynamics. The analysis covers wing aspect ratios from 0.5-3.0 with leading edge sweep of 0.5-4.0 on diamond, circular arc and NACA modified 4-digit airfoils. Nonlinear aerodynamics are approximated with nonlinear zero-lift wave drag curves, yielding results significantly different from those obtained from linear calculations. The analytical technique, useful in preliminary design studies, indicates in all cases that 90 percent of wave drag is generated at the wing apex and trailing edge.

Wood, R. M.↗

The preferred spatial mode of instability for a Mach 2 jet

Phase-averaged schlieren video and an array of azimuthally oriented microphones were used in the experiments performed to determine the preferred spatial structure associated with supersonic nozzle design for an exhaust Mach number of 2. The jet flow was unheated, chemically inert, and submerged in a static environment, conditions that are satisfactory for the quasi-linear wave-analytical model of Tam and Morris (1980) and Tam and Burton (1984). For general conditions of undeterminate phase-averaged optical records, a conditional sampling method was devised, based on fundamental multimode components. This method uncovers the preferred spatial structure, and shows that in addition to the dominant jet flapping mode, there is also a significant contribution from the axisymmetric mode. Near-field correlations with a moving microphone indicate that the flapping plane is nearly stationary, and not spinning as in the Westley and Wolley (1975) experiment.

Seiner, J. M.↗

A computational code for two-dimensional unsteady magnetohydrodynamics by the method of characteristics

A computational code for solving two-dimensional, time-dependent MHD equations by the method of characteristics is presented. Its capabilities are demonstrated by solving two very different problems for which analytical solutions exist: linearized, standing MHD wave motions in a magnetized cylindrical plasma, and nonlinear self-similar expansion of a magnetized plasma ball. The nonlinear development of standing MHD wave solutions in a cylindrical plasma is also studied. The method can be naturally embedded in the computational architecture of massively parallel processors.

Lou, Y. Q.↗

Breaking of the first adiabatic invariants of charged particles in time-dependent magnetic fields - Computer simulations and theory

The mechanics of the first adiabatic invariant mu of nonrelativistic charged particles in time-dependent magnetic inductions B (t) are studied by means of computer simulations and analytic theory. Linear-ramp magnetic-induction profiles are utilized, as well as hyperbolic-tangent ramps and sine half-wave ramps. The change in mu that results from an induction change Delta B that occurs over a time Delta t is quantified for all values of Delta B and Delta t, as well as for all values of the particle position. It is found that the cases fall into two categories with very different mu behavior: cases in which the change in the magnetic induction occurs over a time Delta t that is exactly equal to an integer number of gyroperiods (textbook case) or cases in which the change in the induction occurs over a time Delta t that is not equal to an integer number of gyroperiods (more general case). In both categories mu is an adiabatic invariant, although the conservation of mu is much poorer in the latter category.

Borovsky, Joseph E.↗

A Theoretical Study of the Angular Motions of Spinning Bodies in Space

Euler's dynamic equations were linearized and solved analytically. Analytical expressions which relate angular motions to spin-rate and inertia distributions were obtained and found to be in good agreement with machine solutions of the nonlinear equations for the case of a rectangular-pulse pitching-moment disturbance. Consideration was given to the effects produced by having artificial damping in the system.

Suddath, Jerrold H.↗

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

Muravyov, Alexander A.↗

On the Sensitivity of Atmospheric Ensembles to Cloud Microphysics in Long-Term Cloud-Resolving Model Simulations

Month-long large-scale forcing data from two field campaigns are used to drive a cloud-resolving model (CRM) and produce ensemble simulations of clouds and precipitation. Observational data are then used to evaluate the model results. To improve the model results, a new parameterization of the Bergeron process is proposed that incorporates the number concentration of ice nuclei (IN). Numerical simulations reveal that atmospheric ensembles are sensitive to IN concentration and ice crystal multiplication. Two- (2D) and three-dimensional (3D) simulations are carried out to address the sensitivity of atmospheric ensembles to model dimensionality. It is found that the ensembles with high IN concentration are more sensitive to dimensionality than those with low IN concentration. Both the analytic solutions of linear dry models and the CRM output show that there are more convective cores with stronger updrafts in 3D simulations than in 2D, which explains the differing sensitivity of the ensembles to dimensionality at different IN concentrations.

Zeng, Xiping↗

FRET-Aptamer Assays for Bone Marker Assessment, C-Telopeptide, Creatinine, and Vitamin D

Astronauts lose 1.0 to 1.5% of their bone mass per month on long-duration spaceflights. NASA wishes to monitor the bone loss onboard spacecraft to develop nutritional and exercise countermeasures, and make adjustments during long space missions. On Earth, the same technology could be used to monitor osteoporosis and its therapy. Aptamers bind to targets against which they are developed, much like antibodies. However, aptamers do not require animal hosts or cell culture and are therefore easier, faster, and less expensive to produce. In addition, aptamers sometimes exhibit greater affinity and specificity vs. comparable antibodies. In this work, fluorescent dyes and quenchers were added to the aptamers to enable pushbutton, one-step, bind-and-detect fluorescence resonance energy transfer (FRET) assays or tests that can be freeze-dried, rehydrated with body fluids, and used to quantitate bone loss of vitamin D levels with a handheld fluorometer in the spacecraft environment. This work generated specific, rapid, one-step FRET assays for the bone loss marker C-telopeptide (CTx) when extracted from urine, creatinine from urine, and vitamin D congeners in diluted serum. The assays were quantified in nanograms/mL using a handheld fluorometer connected to a laptop computer to convert the raw fluorescence values into concentrations of each analyte according to linear standard curves. DNA aptamers were selected and amplified for several rounds against a 26- amino acid form of CTx, creatinine, and vitamin D. The commonalities between loop structures were studied, and several common loop structures were converted into aptamer beacons with a fluorophore and quencher on each end. In theory, when the aptamer beacon binds its cognate target (CTx bone peptide, creatinine, or vitamin D), it is forced open and no longer quenched, so it gives off fluorescent light (when excited) in proportion to the amount of target present in a sample. This proportional increase in fluorescence is called a "lights on" FRET response. The vitamin D aptamer beacon gives a "lights off" or inversely proportional fluorescence response to the amount of vitamin D present in diluted serum. These FRET-aptamer assays are rapid (<30 minutes), sensitive (low ng/mL detection limits), and quite easy to carry out (add sample, mix, and detect in the handheld reader). Benefits include the speed of the assays as well as the small amount of space taken up by the handheld reader and cuvette assays. The aptamer DNA sequences represent novel additional features of the existing (patent-pending) FRET-aptamer assay platform.

Bruno, John G.↗

Streamlining the Design Tradespace for Earth Imaging Constellations

Distributed Spacecraft Missions (DSMs) are gaining momentum in their application to Earth Observation (EO) missions owing to their unique ability to increase observation sampling in spatial, spectral, angular and temporal dimensions simultaneously. DSM design includes a much larger number of variables than its monolithic counterpart, therefore, Model-Based Systems Engineering (MBSE) has been often used for preliminary mission concept designs, to understand the trade-offs and interdependencies among the variables. MBSE models are complex because the various objectives a DSM is expected to achieve are almost always conflicting, non-linear and rarely analytical. NASA Goddard Space Flight Center is developing a pre-Phase A tool called "Trade-space Analysis Tool for Constellations" (TAT-C) to initiate constellation mission design. The tool will allow users to explore the tradespace between various performance, cost and risk metrics (as a function of their science mission) and select Pareto optimal architectures that meet their requirements. This paper focuses on the tradespace search and how it can be streamlined by combining physical rules, as well as well-designed orbit and coverage computations, thus yielding significant speed-ups. Two use cases are shown as representative examples of the utility of TAT-C generated trades, and results are preliminarily validated against AGI's Systems Tool Kit.

Science Data Processing↗

A Theoretical Study of the Angular Motions of Spinning Bodies in Space

A theoretical study was made of the angular motions of spinning bodies in space. The analysis was based on Euler's dynamic equations which were linearized and solved analytically. The results of the study are directly applicable only to spin-stabilized vehicles with constant moments of inertia and angular displacements not exceeding about 15 degrees. Simple analytical expressions were obtained which relate angular motions to spin-rate and inertia distributions for a given disturbance. Consideration was given to the effects produced by having artificial damping in the system. The study included numerical examples and comparisons of analytical solutions with machine solutions of exact dynamic equations. The analysis indicated that angular motions are sensitive to inertia distribution. In considering a rectangular-pulse pitching moment, it was found that the residual motion was very sensitive to the time at which the moment was removed. Artificial damping due to a perfect proportional control system seemed to be more advantageous to pencil-like configurations than to disk-like configurations.

Suddath, Jerrold H.↗

Navigating the Deployment and Downlink Tradespace for Earth Imaging Constellations

Distributed Spacecraft Missions (DSMs) are gaining momentum in their application to Earth Observation (EO) missions owing to their unique ability to increase observation sampling in spatial, spectral, angular and temporal dimensions simultaneously. DSM design includes a much larger number of variables than its monolithic counterpart, therefore, Model-Based Systems Engineering (MBSE) has been often used for preliminary mission concept designs, to understand the trade-offs and interdependencies among the variables. MBSE models are complex because the various objectives a DSM is expected to achieve are almost always conflicting, non-linear and rarely analytical. NASA Goddard Space Flight Center (GSFC) is developing a pre-Phase A tool called Tradespace Analysis Tool for Constellations (TAT-C) to initiate constellation mission design. The tool will allow users to explore the tradespace between various performance, cost and risk metrics (as a function of their science mission) and select Pareto optimal architectures that meet their requirements. This paper will describe the different types of constellations that TAT-C’s Tradespace Search Iterator is capable of enumerating (homogeneous Walker, heterogeneous Walker, precessing type, ad-hoc) and their impact on key performance metrics such as revisit statistics, time to global access and coverage. We will also discuss the ability to simulate phased deployment of the given constellations, as a function of launch availabilities and/or vehicle capability, and show the impact on performance. All performance metrics are calculated by the Data Reduction and Metric Computation module within TAT-C, which issues specific requests and processes results from the Orbit and Coverage module. Our TSI is also capable of generating tradespaces for downlinking imaging data from the constellation, based on permutations of available ground station networks - known (default) or customized (by the user). We will show the impact of changing ground station options for any given constellation, on data latency and required communication bandwidth, which in turn determines the responsiveness of the space system.

Nag, Sreeja↗

Inflatable Softgoods Design of an Articulating Crew Transfer Tunnel

Future NASA exploration plans call for lunar and Martian surface systems that form a base camp of multiple, pressurized elements. These discrete components, including habitats and pressurized rovers, require interoperability to meet the Artemis Accords and standard docking systems to physically connect elements together. A pressurized, articulating crew transfer tunnel can be used between a rover and habitat to enable shirt-sleeve transfer of crew and cargo, saving valuable crew time and resources. While transfer tunnels have been described in the past, this work details the design of a structural softgoods system that has compliant capability through a proposed docking range of motion. The inflatable softgoods design is based on a zero-hoop stress shape, known as a Taylor surface, that is stacked and truncated to form a unique and flexible configuration. Analytical, non-linear models have been developed to examine and predict the behavior of the structure, and material testing was used to determine the properties that were used in the model. Finally, a sub-scale test article was constructed using the baseline design and pressurized testing is in work. Additional full-scale testing is planned for future years to fully demonstrate the capability of the system.

Tunnel↗

Inflatable Softgoods Design of an Articulating Crew Transfer Tunnel

Future NASA exploration plans call for lunar and Martian surface systems that form a base camp of multiple, pressurized elements. These discrete components, including habitats and pressurized rovers, require interoperability to meet the Artemis Accords and standard docking systems to physically connect elements together. A pressurized, articulating crew transfer tunnel can be used between a rover and habitat to enable shirt-sleeve transfer of crew and cargo, saving valuable crew time and resources. While transfer tunnels have been described in the past, this work details the design of a structural softgoods system that has compliant capability through a proposed docking range of motion. The inflatable softgoods design is based on a zero-hoop stress shape, known as a Taylor surface, that is stacked and truncated to form a unique and flexible configuration. Analytical, non-linear models have been developed to examine and predict the behavior of the structure, and material testing was used to determine the properties that were used in the model. Finally, a sub-scale test article was constructed using the baseline design and pressurized testing is in work. Additional full-scale testing is planned for future years to fully demonstrate the capability of the system.

Tunnel↗

Recursive linearization of multibody dynamics equations of motion

The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated.

Lin, Tsung-Chieh↗

A method for determining optimum phasing of a multiphase propulsion system for a single-stage vehicle with linearized inert weight

A general analytical treatment is presented of a single-stage vehicle with multiple propulsion phases. A closed-form solution for the cost and for the performance and a derivation of the optimal phasing of the propulsion are included. Linearized variations in the inert weight elements are included, and the function to be minimized can be selected. The derivation of optimal phasing results in a set of nonlinear algebraic equations for optimal fuel volumes, for which a solution method is outlined. Three specific example cases are analyzed: minimum gross lift-off weight, minimum inert weight, and a minimized general function for a two-phase vehicle. The results for the two-phase vehicle are applied to the dual-fuel rocket. Comparisons with single-fuel vehicles indicate that dual-fuel vehicles can have lower inert weight either by development of a dual-fuel engine or by parallel burning of separate engines from lift-off.

Martin, J. A.↗

Mid-frequency Band Dynamics of Large Space Structures

High and low intensity dynamic environments experienced by a spacecraft during launch and on-orbit operations, respectively, induce structural loads and motions, which are difficult to reliably predict. Structural dynamics in low- and mid-frequency bands are sensitive to component interface uncertainty and non-linearity as evidenced in laboratory testing and flight operations. Analytical tools for prediction of linear system response are not necessarily adequate for reliable prediction of mid-frequency band dynamics and analysis of measured laboratory and flight data. A new MATLAB toolbox, designed to address the key challenges of mid-frequency band dynamics, is introduced in this paper. Finite-element models of major subassemblies are defined following rational frequency-wavelength guidelines. For computational efficiency, these subassemblies are described as linear, component mode models. The complete structural system model is composed of component mode subassemblies and linear or non-linear joint descriptions. Computation and display of structural dynamic responses are accomplished employing well-established, stable numerical methods, modern signal processing procedures and descriptive graphical tools. Parametric sensitivity and Monte-Carlo based system identification tools are used to reconcile models with experimental data and investigate the effects of uncertainties. Models and dynamic responses are exported for employment in applications, such as detailed structural integrity and mechanical-optical-control performance analyses.

dynamics↗