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Report discusses enhanced projection-and-assembly (EP&A) method and its application to Galileo spacecraft. EP&A method and its predecessor, projection-and-assembly (P&A) method, described in "Enhanced Method of Reduction of Mathematical Models" (NPO-18402), and "Two-Stage Reduction of Dynamical Models" (NPO-18723).
This paper explains the projection and assembly model reduction method which has been used to derive reduced order component models for the Galileo spacecraft. Assembly of reduced order component models produces a reduced order system model which can then be used in multibody simulation codes for efficient run times. The methodology is explained and a proof is given showing the exact reproduction of selected significant system modes. Frequency bounds are obtained for all modes produced when the reduced order components are assembled. The projection and assembly method is demonstrated on two examples. The first example is a simplified model of the Galileo spacecraft, while the second example is the model of the Galileo spacecraft in its early mission configuration. When articulation of components is allowed, the method may not reproduce all system modes precisely. Remedies for this problem are suggested.
An overview of projection methods based on Krylov subspaces are given with emphasis on their application to solving matrix equations that arise in control problems. The main idea of Krylov subspace methods is to generate a basis of the Krylov subspace Span and seek an approximate solution the the original problem from this subspace. Thus, the original matrix problem of size N is approximated by one of dimension m typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now just becoming popular for solving nonlinear equations. It is shown how they can be used to solve partial pole placement problems, Sylvester's equation, and Lyapunov's equation.
The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.
An efficient solution procedure for time-accurate solutions of Incompressible Navier-Stokes equation is obtained. Artificial compressibility method requires a fast convergence scheme. Pressure projection method is efficient when small time-step is required. The number of sub-iteration is reduced significantly when Poisson solver employed with the continuity equation. Both computing time and memory usage are reduced (at least 3 times). Other work includes Multi Level Parallelism (MLP) of INS3D, overset connectivity for the validation case, experimental measurements, and computational model for boost pump.
We developed a parallel, numerically accurate and stable, and computationally efficient finate-difference incompressible Navier-Stokes (N-S) fluid flow solver. The solver runs on both sequential and massively parallel computers. The numerical method used here is a second-order projection method on a staggered grid. The code is highly modular and it can be used either as a stand-alone flow solver and or a template code which can be adapted or expanded to a specific application. Numerical results and parallel performances of our code on Intel Delta and Paragon are reported.
This presentation focuses on project management, specifically addressing project issues using the scientific method of problem-solving. Two sample projects where this methodology has been applied are provided.
Paper presents mathematical comparison of several techniques with the limiting slope technique for data reduction and reconstruction. Limiting slope method results in maximum possible RMS error versus data compression ratio advantage of 2-to-1 over step and fan methods and 3-to-1 over the two point projection method.
NASA has funded several major programs (the Probabilistic Structural Analysis Methods Project is an example) to develop probabilistic structural analysis methods and tools for engineers to apply in the design and assessment of aerospace hardware. A probabilistic finite element software code, known as Numerical Evaluation of Stochastic Structures Under Stress, is used to determine the reliability of a critical weld of the Space Shuttle solid rocket booster aft skirt. An external bracket modification to the aft skirt provides a comparison basis for examining the details of the probabilistic analysis and its contributions to the design process. Also, analysis findings are compared with measured Space Shuttle flight data.
For 50 years, NASA's journeys into air and space have developed humankind's understanding of the universe, advanced technology breakthroughs, enhanced air travel safety and security, and expanded the frontiers of scientific research. These accomplishments share a common genesis: education. Education is a fundamental element of NASA's activities, reflecting a balanced and diverse portfolio of: Elementary and Secondary Education, Higher Education, e-Education, Informal Education, and Minority University Research and Education Programs (MUREP). Previous experience has shown that implementing exciting and compelling NASA missions are critical to inspiring the next generation of explorers, innovators, and leaders. Through partnerships with the Agency's Mission Directorates, other federal agencies, private industries, scientific research, and education/academic organizations, NASA's unique mission and education initiatives (content, people, and facilities) are helping to spark student interest and to guide them toward careers in science, technology, engineering, and mathematics (STEM). NASA continues to inspire the next generation of explorers, innovators, and future leaders through its educational investments, which are designed to: (1) Strengthen NASA and the Nation's future workforce -- NASA will identify and develop the critical skills and capabilities needed to ensure achievement of exploration, science, and aeronautics. (2) Attract and retain students in STEM disciplines through a progression of educational opportunities for students, teachers, and faculty -- To compete effectively for the minds, imaginations, and career ambitions of America's young people, NASA will focus on engaging and retaining students in STEM education programs to encourage their pursuit of educational disciplines critical to NASA's future engineering, scientific, and technical missions. 3. Engage Americans in NASA's mission -- NASA will build strategic partnerships and links between formal and informal STEM education providers. Through hands-on, interactive, educational activities, NASA will engage students, educators, families, the general public, and all agency stakeholders in increasing America's science and technology literacy. NASA Education uses multiple methods to assess and evaluate the success of its programs and projects. Methods include strategic planning, management and control, expert evaluations and assessments, competitive acquisition, and analysis of performance measurement data and metrics. Additional control measures are in development. These measures will further improve data collection, assist in assessing return on investments, and provide information for accountability in project and program management. In 2009, NASA directly reached over one million students and over 115,000 educators.
Inflow projections provide scenarios for future water availability and are integral to operational reservoir management. They can aid water practitioners in decision-making for conservation efforts, multiyear storage retention, managing flood risk, downstream water releases, and regional growth planning. However, conventional methods are often limited in terms of their ability to incorporate non-stationarity, long run persistence, and the cross-correlation of multiple series in a region. This research aims to address these issues with a hybrid approach that integrates Empirical Mode Decomposition (EMD) with the Matalas multisite generation method. Multiple long-run inflows were examined for the Shasta/Trinity Reservoirs and Oroville Reservoir of California. EMD is used to decompose each inflow series into a set of independent intrinsic mode functions (IMFs) that have different timescales and frequencies. These IMFs were grouped into intradecadal (less-than- 10-year average periodicity) and interdecadal (greater-than-10-year average periodicity) series for each site. The IMF projections at each site were then combined to produce replicates of the historical data. This preserves the correlation structure of the intra- and interdecadal components of the series. The hybrid EMD-Matalas method was compared to a traditional autoregressive lag-one model. Both methods were found to retain the statistical characteristics of the historical data. However, the EMD-Matalas method retained the multiyear wet and dry periods to a greater degree. This was examined by comparing the 5-year and 10-year sums from the traditional model with the hybrid EMD-Matalas model. An advantage of the EMD-Matalas method is the ability to explicitly incorporate modes of non-stationary long-run persistence often associated with large-scale climate drivers such as the El Nino Southern Oscillation (ENSO) or the Pacific Decadal Oscillation (PDO). This contributes to scenario planning that may be particularly important for managing multiyear low flow periods.
Satellite altimetry measurements have provided global, evenly distributed observations of the ocean surface since 1993. However, the difficulties introduced by the presence of model biases and the requirement that data assimilation systems extrapolate the sea surface height (SSH) information to the subsurface in order to estimate the temperature, salinity and currents make it difficult to optimally exploit these measurements. This talk investigates the potential of the altimetry data assimilation once the biases are accounted for with an ad hoc bias estimation scheme. Either steady-state or state-dependent multivariate background-error covariances from an ensemble of model integrations are used to address the problem of extrapolating the information to the sub-surface. The GMAO ocean data assimilation system applied to an ensemble of coupled model instances using the GEOS-5 AGCM coupled to MOM4 is used in the investigation. To model the background error covariances, the system relies on a hybrid ensemble approach in which a small number of dynamically evolved model trajectories is augmented on the one hand with past instances of the state vector along each trajectory and, on the other, with a steady state ensemble of error estimates from a time series of short-term model forecasts. A state-dependent adaptive error-covariance localization and inflation algorithm controls how the SSH information is extrapolated to the sub-surface. A two-step predictor corrector approach is used to assimilate future information. Independent (not-assimilated) temperature and salinity observations from Argo floats are used to validate the assimilation. A two-step projection method in which the system first calculates a SSH increment and then projects this increment vertically onto the temperature, salt and current fields is found to be most effective in reconstructing the sub-surface information. The performance of the system in reconstructing the sub-surface fields is particularly impressive for temperature, but not as satisfactory for salt.
The results are presented for the stagnation-point heat-transfer rates used in the design process of the Aeroassist Flight Experiment (AFE) vehicle over its entire aeropass trajectory. The prediction methods used in this investigation demonstrate the application of computational fluid dynamics (CFD) techniques to a wide range of flight conditions and their usefulness in a design process. The heating rates were computed by a viscous-shock-layer (VSL) code at the lower altitudes and by a Navier-Stokes (N-S) code for the higher altitude cases. For both methods, finite-rate chemically reacting gas was considered, and a temperature-dependent wall-catalysis model was used. The wall temperature for each case was assumed to be radiative equilibrium temperature, based on total heating. The radiative heating was estimated by using a correlation equation. Wall slip was included in the N-S calculation method, and this method implicitly accounts for shock slip. The N-S/VSL combination of projection methods was established by comparison with the published benchmark flow-field code LAURA results at lower altitudes, and the direct simulation Monte Carlo results at higher altitude cases. To obtain the design heating rate over the entire forward face of the vehicle, a boundary-layer method (BLIMP code) that employs reacting chemistry and surface catalysis was used. The ratio of the VSL or N-S method prediction to that obtained from the boundary-layer method code at the stagnation point is used to define an adjustment factor, which accounts for the errors involved in using the boundary-layer method.
Propellant slosh is a potential source of disturbance that can significantly impact the stability of space vehicles. The slosh dynamics are typically represented by a mechanical model of a spring-mass-damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control analysis. The typical parameters required by the mechanical model include natural frequency of the slosh, slosh mass, slosh mass center location, and the critical damping ratio. A fundamental study has been undertaken at NASA MSFC to understand the fluid damping physics from a ring baffle in the barrel section of a propellant tank. An asymptotic damping equation and CFD blended equation have been derived by NASA MSFC team to complement the popularly used Miles equation at different flow regimes. The new development has found success in providing a nonlinear damping model for the Space Launch System. The purpose of this study is to further extend the semi-empirical damping equations into the oblate spheroidal dome section of the propellant tanks. First, previous experimental data from the spherical baffled tank are collected and analyzed. Several methods of taking the dome curvature effect, including a generalized Miles equation, area projection method, and equalized fill height method, are assessed. CFD simulation is used to shed light on the interaction of vorticity around the baffle with the locally curved wall and liquid-gas interface. The final damping equation will be validated by a recent subscale test with an oblate spheroidal dome conducted at NASA MSFC.
NASA's Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission will make global ocean color and atmospheric measurements to provide extended data records of ocean ecology and global biogeochemistry, along with polarimetric measurements for advanced observations of aerosols, clouds and the ocean. PACE will contain three instruments: the primary Ocean Color Instrument (OCI), and two multi-angle polarimeters (MAPs). The latter instruments are contributed under a ‘Do-No-Harm’ (to the rest of the PACE mission) principle, and the PACE Science Data Processing System (SDPS) is only required to produce Level-1b (geolocated radiances with calibration applied) data without performance requirements. However, there is a strong desire to produce data in a format that merges the disparate spatial resolutions, viewing geometry and sampling nature of the three instruments. Our terminology for this format is Level 1c (L1C). This format will be an input to Level 2 algorithms produced from standalone MAP instrument observations, or from algorithms employing multi-sensor fusion. Creating the L1C format has several components. This includes choice of projection method, the means by which multi-angle views are properly incorporated into that projection (‘aggregation’) the means to represent wavelength and light polarization state, the selection of data to be included within the L1C file, and the handling of ancillary data either required for L1C file generation or needed in that format for L2 processing.
Methods for pre-screening stress constraints into either primary or side-constraint categories are reviewed; a projection method, which is developed from prior cycle stress resultant history, is introduced as an additional screening parameter. Stress resultant projections are also employed to modify the traditional stress-ratio, side-constraint boundary. A special application of structural modification reanalysis is applied to the critical stress constraints to provide feasible designs that are preferable to those obtained by conventional scaling. Sample problem executions show relatively short run times and fewer design cycle iterations to achieve low structural weights; those attained are comparable to the minimum values developed elsewhere.
The present novel algorithm for 3D incompressible Navier-Stokes equations treats a domain which is (1) infinite in the vertical direction, using a mapped spectral method; (2) finite in the streamwise direction, using a classical Fourier method; and (3) homogeneous in the spanwise direction, using high-order compact finite differencing. A projection method is employed which ensures the exact conservation of mass, as well as the satisfaction of the boundary conditions at infinity. The novel aspects of these methods are noted, and the code they constitute is validated in light of several test cases. Results are presented for two- and three-dimensional mixing layers.
The purpose of this study is to investigate the flow and heat transfer characteristics of a combined forced and free convection flow in a curved duct. Solutions are obtained by solving the low Mach number model of the Navier-Stokes equation using a control volume method. The finite-volume method was developed with the use of a predictor-corrector numerical scheme and some new variations of the classical projection method. Solutions indicated that the existence of a buoyancy force has changed the entire flow structure inside a curved duct. Reversed flow at both inner and outer bend is observed. For moderate Reynolds number, the upstream section of the duct was significantly influenced by the free convection processes. In general, heat transfer is strong at the inner bend of the beginning of the heated section and at the outer bend on the last half of the heated section. The maximum velocity location is strongly influenced by the combined effects of buoyancy and centrifugal forces. A strong buoyancy force can reduce the strength of the secondary flow where it plays an important role in mixing.