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NASA NTRS1983

Low-level water vapor fields from the VISSR Atmospheric Sounder (VAS) 'split window' channels

A simple physical algorithm is presented which calculates the water vapor content of the lower troposphere from the 11 and 12 micron (split window) channels on the VISSR Atmospheric Sounder (VAS) on the Geostationary Operational Environmental Satellites. The algorithm is used to analyze a time series of VAS split window radiances observed at 15 km horizontal resolution over eastern North America during a 12 hr period on 13 July 1981. Results of the color coded images of the derived precipitable water fields are found to show vivid water vapor features whose broad structure and evolution are verified by the radiosonde and surface networks. The satellite moisture fields also show significant mesoscale features and rapid developments which are not resolved by the conventional networks. The VAS split window is determined to clearly differentiate those areas in which water vapor extends over a deep layer and is more able to support convective cells from those areas in which water vapor is confined to a shallow layer and is therefore less able to support convection. It is concluded that the VAS split windows can be used operationally to monitor mesoscale developments in the low-level moisture fields over relatively cloud-free areas of the United States.

Chesters, D.↗

NASA NTRS1998

Evaluation of Terms in the Water Vapor Budget Using Airborne Dial and In Situ Measurements from the Southern Great Plans 1997 Experiment

The Southern Great Plains (SGP97) field experiment was conducted in Oklahoma during June and July 1997 primarily to validate soil moisture retrieval algorithms using microwave radiometer measurements from aircraft as well as in situ surface measurements. One important objective of the SGP97 experiment plan was to examine the effect of soil moisture on the evolution of the atmospheric boundary layer (ABL) and clouds over the Southern Great Plains during the warm season. To support boundary layer studies during SGP97. the NASA Langley Research Center's Lidar Atmospheric Sensing Experiment (LASE) was flown on a NASA-P3 aircraft in conjunction with the Electronically Scanned Thinned Array Radiometer (ESTAR). The LASE instrument is an airborne, downward-looking differential absorption lidar (DIAL) system capable of measuring water vapor concentration as well as aerosol backscatter with high horizontal and vertical resolution in the ABL. Here, we will demonstrate how the LASE data can be used to determine water vapor statistics and most of the water vapor budget terms in the ABL. This information can then be related to spatial variations in soil moisture and the surface energy budget. The extensive surface and aircraft in situ measurements conducted during SGP97 provide information on the ABL that cannot be retrieved from the LASE data alone and also offer an excellent opportunity to validate the remote water vapor budget measurements with LASE.

Senff, Christoph J.↗

NASA NTRS1987

Analysis of the Continuous Stellar Tracking Attitude Reference (CSTAR) attitude rate processor

The Continuous Stellar Tracking Attitude Reference (CSTAR) system is an in-house project for Space Station to provide high accuracy, drift free attitude and angular rate information for the GN&C system. The outputs of the solid state star trackers are processed to provide attitude information; rate data is then derived from the attitude. Rate derivation is based on discrete time polynomial approximation techniques. This gives simple algorithms which allow for interpolation by other users. Attitude rate is modeled as a constant with low amplitude, low frequency sinusoids superimposed. The rate processor is parameterized to account for the effects of random errors, sample rate, data processing rate and perturbation frequency. The baseline system may be characterized as follows: the three sigma attitude accuracy is 0.01 degrees, the three sigma rate accuracy is 0.0001 degrees per second, the sample rate is 100 Hertz, the sampled signal is bandlimited to 0.5 Hertz, and the data processing rate is 10 Hertz. The above system requires a differentiator of length 127. This will track rate perturbations of frequencies less than 0.01 Hertz with low systematic errors.

Uhde-Lacovara, J.↗

NASA NTRS1995

Analysis of composite ablators using massively parallel computation

In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

Shia, David↗

NASA NTRS2008

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

Swanson, R. C.↗

NASA NTRS2001

Optical Measurements and Modeling to Estimate Concentrations and Fluxes of Organic Matter in the Southern Ocean

This project was a collaboration between two Principal Investigators, Dr. Dariusz Stramski and Dr. Greg Mitchell of Scripps Institution of Oceanography, University of California San Diego. Our overall goal was to conduct optical measurements and modeling to estimate concentrations of organic matter in the Southern Ocean in support of the U.S. JGOFS Process Study in this region. Key variables and processes of high relevance to accomplish the JGOFS goals include time and space resolution of phytoplankton pigments, particulate organic carbon, and the formation and export of organic carbon. Our project focused on establishing the fundamental relationships for parameterization of these variables and processes in terms of the optical properties of seawater, and developing understanding of why the Southern Ocean differs from other low-latitude systems, or has differentiation within. Our approach builds upon historical observations that optical properties provide a useful proxy for key reservoirs of organic matter such as chlorophyll alpha (Chl) and particulate organic carbon (POC) concentrations, which are of relevance to the JGOFS objectives. We carried out detailed studies of in situ and water sample optical properties including spectral reflectance, absorption, beam attenuation, scattering, and backscattering coefficients. We evaluated the ability to estimate Chl from the spectral reflectance (ocean color) in the Southern Ocean. We examined relationships between the ocean optical properties and particulate organic carbon. We developed, for the first time, an algorithm for estimating particulate organic carbon concentration in the surface ocean from satellite imagery of ocean color. With this algorithm, we obtained maps of POC distribution in the Southern Ocean showing the seasonal progression of POC in the austral spring-summer season. We also developed a semianalytical reflectance model for the investigated polar waters based on our field measurements of absorption and backscattering coefficients and Chl-dependent parameterizations of these coefficients. With this model, libraries of expected reflectance spectra for various chlorophyll concentrations can be generated with high spectral resolution for specific oceanic regions. In addition, our semianalytical reflectance model provided insight into the mechanisms which drive the empirical relationships between the ocean color and chlorophyll concentration. Our optical approach to the study of pigment and carbon concentrations will be directly relevant to development of system models and long-term monitoring of the Southern Ocean.

Stramski, Dariusz↗

NASA NTRSDate not supplied

Progress on Inverse Estimation Technique of Non-Linear Pitch Damping Coefficient Curves Using Free-Flight CFD Generated Trajectories

Characterization of entry vehicle pitch damping coefficient curves is crucial to ensure appropriate re-entry and overall mission success. The pitch damping coefficient (C_(m_q )+C_(m_α ̇ )) is used to encapsulate the oscillatory growth or decay of a body during a trajectory. The inverse estimation technique utilizes an existing Free-Flight CFD (FF-CFD) dataset and wraps a reconstruction algorithm in an optimizer. The reconstruction integrates the planar equations of motion derived by Schoenenberger, Queen [1] using Python’s scipy.integrate.solve_ivp. The optimizer’s objective function is the normalized 𝐿2 residual of the angle of attack peaks between the reconstructed trajectory and the original data produced with FF-CFD. Inclusion of the peak times in this residual calculation allows for simultaneous optimization of the pitch moment coefficient, C_(m_α ). This residual equation is shown below in Eq. 1. The optimizer scipy.optimize.minimize was used with the gradient-based Powell method for the analysis presented, however the differential evolution method was investigated as means of comparison, and was found to produce marginally lower residual values with prohibitively longer run times. Further, the pitch damping curve is found by fitting a cubic interpolation function to a set of (α, (C_(m_q )+C_(m_α ̇ ))) control points, where the α points are held constant and the (C_(m_q )+C_(m_α ̇ )) values are the optimized parameters. The pitch moment curve uses a linear interpolation between the minimum and maximum α in the dataset. FF-CFD generated trajectories using the Dragonfly capsule geometry with the Genesis ballistic range model parameters were simulated and used for this analysis. These FF-CFD trajectories simulate planar motion, as restricted by the reconstructing the equations of motion, of three different cases: 1-DoF (free-to-pitch), 2-DoF (free-to-pitch and heave), and 3-DoF (free-to-pitch, heave, and decelerate). Pitch damping coefficient curves generated using this inverse estimation curve technique with FF-CFD 1-DoF Dragonfly data are found in Fig. 1. Preliminary results reconstructing ballistic range shots using these FF-CFD derived predictions of the pitch damping curve (Fig. 1) are shown in Fig. 2. It should be noted that the ballistic range shot used a Genesis model whereas the FF-CFD data used a Dragonfly geometry, however these geometries are similar.

entry↗

NASA NTRS1991

Comparison of SMAC, PISO, and iterative time-advancing schemes for unsteady flows

Calculations of unsteady flows using a simplified marker and cell (SMAC), a pressure implicit splitting of operators (PSIO), and an iterative time advancing scheme (ITA) are presented. A partial differential equation for incremental pressure is used in each time advancing scheme. Example flows considered are a polar cavity flow starting from rest and self-sustained oscillating flows over a circular and a square cylinder. For a large time step size, the SMAC and ITA are more strongly convergent and yield more accurate results than PSIO. The SMAC is the most efficient computationally. For a small time step size, the three time advancing schemes yield equally accurate Strouhal numbers. The capability of each time advancing scheme to accurately resolve unsteady flows is attributed to the use of new pressure correction algorithm that can strongly enforce the conservation of mass. The numerical results show that the low frequency of the vortex shedding is caused by the growth time of each vortex shed into the wake region.

Kim, Sang-Wook↗

NASA NTRS1992

Comparison of the SMAC, PISO, and iterative time-advancing schemes for unsteady flows

Calculations of unsteady flows using a simplified marker and cell (SMAC), a pressure implicit splitting of operators (PISO), and an iterative time advancing scheme (ITA) are presented. A partial differential equation for incremental pressure is used in each time advancing scheme. Example flows considered are a polar cavity flow starting from rest and self-sustained oscillating flows over a circular and a square cylinder. For a large time step size, the SMAC and ITA are more strongly convergent and yield more accurate results than PISO. The SMAC is the most efficient computationally. For a small time step size, the three time advancing schemes yield equally accurate Strouhal numbers. The capability of each time advancing scheme to accurately resolve unsteady flows is attributed to the use of new pressure correction algorithm that can strongly enforce the conservation of mass. The numerical results show that the low frequency of the vortex shedding is caused by the growth time of each vortex shed into the wake region.

Kim, S.-W.↗

NASA NTRS1988

Minimal parameter solution of the orthogonal matrix differential equation

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS1988

Minimal parameter solution of the orthogonal matrix differential equation

Baritzhack, Itzhack Y.↗

NASA NTRS1990

Minimal parameter solution of the orthogonal matrix differential equation

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed emplying the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Bar-Itzhack, Itzhack Y.↗

NASA NTRSDate not supplied

Towards Erecting Straighter Lightweight Towers on the Moon Using Deployable Guy Wires

This paper reports our static stability test findings for a simple guy wire system to correct the natural lateral deflections of an 8.5m tall, compact deployable composite tower intended to support exploration of lunar permanently shadowed regions by nearby robotic assets. Deployable composite booms with microgravity flight heritage are currently being investigated at NASA Langley Research Center (LaRC) and Massachusetts Institute of Technology(MIT)’s Space Resources Workshop for their potential to be vertically deployed in the lunar gravity field, in support of NASA’s Artemis campaign. These applications include vertical solar arrays and the provision of elevated lines-of-sight to science or engineering payloads on landers and rovers, in support of nearby or distant crewed or robotic assets exploring scientifically interesting and hard to reach areas. Useful elevated payloads include radio repeaters, remote sensing and imaging, navigation and power beaming systems. However, while these lightweight booms have an excellent height to mass ratio, they typically exhibit slight axial curvature upon deployment resulting in appreciable lateral dead-load deflection of the tip mass relative to the tower base. This static deflection increases with tower height and tip mass, not only constraining the value delivered by the tower but also endangering its integrity. To develop a competitive, lightweight deployable composite boom tower, a capability to correct static deflections during and after deployment may be required. This paper presents a pathfinder deployable guy wire stability system for the MIT / LaRC self-erecting composite boom lunar tower that provides real time measurements, maintains tension passively, and can serve as a reconfigurable platform to test new guy wire components, configurations and control algorithms. Using a validated, calibrated photogrammetry system, the natural lateral deflection of the boom tip relative to the boom base at different deployed heights in Earth’s gravity field was recorded. With real-time tension measurements it was found that guy wires can significantly reduce the tip deflection of a deployable composite boom under dead load. Specifically, we found that (1) control capability is greatest where it is needed most, i.e. for the lever arm closest to being opposite the direction of deflection, and (2) for a tower height of at least 8.5 m and arm length of at least 60 cm, a solution of differential tension in all three arms exists and, in principle, provides sufficient control capability to correct or significantly reduce boom deflections. We also found that natural deflections occur almost entirely out-of-plane of the seams of the boom cross-section, which was expected, and that the natural boom tip lateral deflection under dead load upon deployment was ~5% of boom deployed length, unexpectedly exceeding the manufacturing acceptance specification of 1%.Ongoing and future collaborative work between LaRC and MIT includes the further investigation of the unexpected lateral deflection, testing of alternative guy wire system designs at higher tensions and higher deployed heights, as well as trade studies of costs and benefits of an optimized integrated guywire system compared to other types of static stability solutions.

lunar towers↗

NASA NTRS2004

Computations of Wall Distances Based on Differential Equations

The use of differential equations such as Eikonal, Hamilton-Jacobi and Poisson for the economical calculation of the nearest wall distance d, which is needed by some turbulence models, is explored. Modifications that could palliate some turbulence-modeling anomalies are also discussed. Economy is of especial value for deforming/adaptive grid problems. For these, ideally, d is repeatedly computed. It is shown that the Eikonal and Hamilton-Jacobi equations can be easy to implement when written in implicit (or iterated) advection and advection-diffusion equation analogous forms, respectively. These, like the Poisson Laplacian term, are commonly occurring in CFD solvers, allowing the re-use of efficient algorithms and code components. The use of the NASA CFL3D CFD program to solve the implicit Eikonal and Hamilton-Jacobi equations is explored. The re-formulated d equations are easy to implement, and are found to have robust convergence. For accurate Eikonal solutions, upwind metric differences are required. The Poisson approach is also found effective, and easiest to implement. Modified distances are not found to affect global outputs such as lift and drag significantly, at least in common situations such as airfoil flows.

Tucker, Paul G.↗

NASA NTRS1992

Domain decomposition: A bridge between nature and parallel computers

Domain decomposition is an intuitive organizing principle for a partial differential equation (PDE) computation, both physically and architecturally. However, its significance extends beyond the readily apparent issues of geometry and discretization, on one hand, and of modular software and distributed hardware, on the other. Engineering and computer science aspects are bridged by an old but recently enriched mathematical theory that offers the subject not only unity, but also tools for analysis and generalization. Domain decomposition induces function-space and operator decompositions with valuable properties. Function-space bases and operator splittings that are not derived from domain decompositions generally lack one or more of these properties. The evolution of domain decomposition methods for elliptically dominated problems has linked two major algorithmic developments of the last 15 years: multilevel and Krylov methods. Domain decomposition methods may be considered descendants of both classes with an inheritance from each: they are nearly optimal and at the same time efficiently parallelizable. Many computationally driven application areas are ripe for these developments. A progression is made from a mathematically informal motivation for domain decomposition methods to a specific focus on fluid dynamics applications. To be introductory rather than comprehensive, simple examples are provided while convergence proofs and algorithmic details are left to the original references; however, an attempt is made to convey their most salient features, especially where this leads to algorithmic insight.

Keyes, David E.↗

NASA NTRS2012

High Resolution Observations of Drop Size Distribution for GPM Ground Validation

During the Mid-latitude Continental Convective Cloud Experiment (MC3E), NASA's GPM GV Disdrometer and Radar Observations of Precipitation (DROP) Facility deployed an array of disdrometers and rain gauges in northern Oklahoma to sample, with high resolution, the drop size distribution for use in development of precipitation retrieval algorithms for the GPM core satellites. The DROP Facility instruments deployed during MC3E consisted of 16 autonomous Parsivel units, 5 two-dimensional video disdrometers (2dvds), a vertically pointing K band radar, and 32 tipping bucket rain gauges. There were several rainfall events during MC3E in which rain drops exceeding 6 mm in diameter were recorded. The disdrometer array revealed large rain drops with diameters exceeding 6 mm and 8 mm during two separate stratiform and convective rainfall events, respectively. The NPOL radar, which was scanning in high resolution RHI mode (every 40 sec) over the disdrometer array during the stratiform event, indicated a 1 km thick bright band with a differential reflectivity column of 2-3 dB extending below the melting layer to the surface where the large drops were recorded by the 2dvds. These large drops are important for GPM since they can have a great impact upon satellite precipitation retrieval, especially near the ground and below heavy convective rainfall cores where satellites have had problems depicting the rainfall.

Gatlin, Patrick N.↗

NASA NTRS1978

A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations

Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.

Kurtz, L. A.↗

NASA NTRS1990

Dual-shaped offset reflector antenna designs from solutions of the geometrical optics first-order partial differential equations

In obtaining solutions to the first-order nonlinear partial differential equations (PDEs) for synthesizing offset dual-shaped reflectors, it is found that previously observed computational problems can be avoided if the integration of the PDEs is started from an inner projected perimeter and integrated outward rather than starting from an outer projected perimeter and integrating inward. This procedure, however, introduces a new parameter, the main reflector inner perimeter radius p(o), when given a subreflector inner angle 0(o). Furthermore, a desired outer projected perimeter (e.g., a circle) is no longer guaranteed. Stability of the integration is maintained if some of the initial parameters are determined first from an approximate solution to the PDEs. A one-, two-, or three-parameter optimization algorithm can then be used to obtain a best set of parameters yielding a close fit to the desired projected outer rim. Good low cross-polarization mapping functions are also obtained. These methods are illustrated by synthesis of a high-gain offset-shaped Cassegrainian antenna and a low-noise offset-shaped Gregorian antenna.

Galindo-Israel, V.↗