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NASA NTRS2002

Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

Freed, Alan D.↗
NASA NTRS2001

Impact of Quikscat Data on Numerical Weather Prediction

Scatterometer observations of the ocean surface wind speed and direction improve the depiction and prediction of storms at sea. These data are especially valuable where observations are otherwise sparse ---mostly in the Southern Hemisphere and tropics, but also on occasion in the North Atlantic and North Pacific. The SeaWinds scatterometer on the QuikScat satellite was launched in July 1999 and it represents a dramatic departure in design from the other scatterometer instruments launched during the past decade (ERS-1,2 and NSCAT). The NASA Data Assimilation Office (DAO) was the first data assimilation center to assimilate QuikScat SeaWinds data and evaluate their impact on numerical weather prediction. Several data impact experiments have been performed, using systems from both the DAO (GEOS-3) and from NCEP (GDAS). In general, these experiments have shown a modest impact of SeaWinds data on numerical weather prediction, the magnitude of which appears to be comparable to the magnitude of the impact of AMI scatterometer data from the ERS satellites. Some of the main results from these experiments will be presented at the meeting.

Atlas, Robert↗
NASA NTRS1995

Numerical Methodology For Full-Body TPS Sizing And Optimization For Access-To-Space Vehicles

This paper presents details of the methodology and numerical procedures developed at NASA Ames for full-body TEXAS sizing and optimization for Access to Space vehicle concepts. The core of the procedures is a robust implicit solver for one dimensional transient heat conduction in reusable multilayer TEXAS stackups. The solver includes an arbitrary number of material layers, contact resistances between materials, temperature and pressure dependent material and surface properties, numerous boundary-condition options, and self-adaptive time stepping. The solver is coupled with the Access-to-Space material database of 23 candidate TPS and structural materials and a thermal-environment database obtained from trajectory-based fullbody Navier-Stokes computations of the external flowfield. The thermal environment and material response are coupled through the use of T-type heat transfer coefficients. TIPS sizing and weight optimization are performed at every surface point on the vehicle based on sizing constraints which include material temperature limits, maximum backwall temperature, and cumulative interior heat flux. Typical results are presented for a lifting body concept with 10000 surface points, which required 35 minutes to compute on an SGI Indigo 2.

Milos, Frank S.↗
NASA NTRS1999

1-D Numerical Analysis of ABCC Engine Performance

ABCC engine combines air breathing and rocket engine into a single engine to increase the specific impulse over an entire flight trajectory. Except for the heat source, the basic operation of the ABCC is similar to the basic operation of the RBCC engine. The ABCC is intended to have a higher specific impulse than the RBCC for single stage Earth to orbit vehicle. Computational fluid dynamics (CFD) is a useful tool for the analysis of complex transport processes in various components in ABCC propulsion system. The objective of the present research was to develop a transient 1-D numerical model using conservation of mass, linear momentum, and energy equations that could be used to predict flow behavior throughout a generic ABCC engine following a flight path. At specific points during the development of the 1-D numerical model a myriad of tests were performed to prove the program produced consistent, realistic numbers that follow compressible flow theory for various inlet conditions.

Holden, Richard↗
NASA NTRS1997

Direct Numerical Simulation of Supersonic Turbulent Boundary Layers

The talk will present some initial results from the direct numerical simulation (DNS) of compressible turbulent boundary layers. We solve numerically the compressible Navier-Stokes equations using a method based on Spalart's transformation for the incompressible turbulent boundary layer. This allows the spatially developing boundary layer to be transformed to a calculation with periodic boundary conditions in the streamwise and spanwise directions. The equations are solved using Fourier expansions in the horizontal directions and B-splines in the wall-normal direction. The first simulation is at Mach 2.5 with a momentum thickness Reynolds number based on wall viscosity of R(sub theta(sup 1)) = 825. We are examining the physics of the compressible boundary layer using turbulence statistics and budget equations. The turbulence statistics include: rms (root mean square) and mean profiles, energy spectra, and two-point correlations. It is found that there are large density gradients which require significantly more resolution than the incompressible case.

Guarini, Stephen↗
NASA NTRS2002

Numerical Filtering of Spurious Transients in a Satellite Scanning Radiometer: Application to CERES

The Clouds and Earth Radiant Energy System (CERES) scanning, radiometer was designed to provide high accuracy measurements of the radiances from the earth. Calibration testing of the instruments showed the presence of all undesired slow transient in the measurements of all channels at 1% to 2% of the signal. Analysis of the data showed that the transient consists of a single linear mode. The characteristic time of this mode is 0.3 to 0.4 s and is much greater than that the 8-10-ms response time of the detector, so that it is well separated from the detector response. A numerical filter was designed for the removal of this transient from the measurements. Results show no trace remaining of the transient after application of the numerical filter. The characterization of the slow mode on the basis of ground calibration data is discussed and flight results are shown for the CERES instruments aboard the Tropical Rainfall Measurement Mission and Terra spacecraft. The primary influence of the slow mode is in the calibration of the instrument and the in-flight validation of the calibration. This method may be applicable to other radiometers that are striving for high accuracy and encounter a slow spurious mode regardless of the underlying physics.

Smith, G. Louis↗
NASA NTRS1997

On the Numerical Prediction of Flow Transition

Knowledge from dynamical systems theory is used to study numerical uncertainties in direct numerical simulation of transition from laminar to turbulent flows. Spurious behavior due to underresolved grids and temporal discretizations is illustrated with 2-D CFD simulations.

Yee, H. C.↗
NASA NTRS2002

2001 Numerical Propulsion System Simulation Review

The technologies necessary to enable detailed numerical simulations of complete propulsion systems are being developed at the NASA Glenn Research Center in cooperation with industry, academia and other government agencies. Large scale, detailed simulations will be of great value to the nation because they eliminate some of the costly testing required to develop and certify advanced propulsion systems. In addition, time and cost savings will be achieved by enabling design details to be evaluated early in the development process before a commitment is made to a specific design. This concept is called the Numerical Propulsion System Simulation (NPSS). NPSS consists of three main elements: (1) engineering models that enable multidisciplinary analysis of large subsystems and systems at various levels of detail, (2) a simulation environment that maximizes designer productivity, and (3) a cost-effective, high-performance computing platform. A fundamental requirement of the concept is that the simulations must be capable of overnight execution on easily accessible computing platforms. This will greatly facilitate the use of large-scale simulations in a design environment. This paper describes the current status of the NPSS with specific emphasis on the progress made over the past year on air breathing propulsion applications. Major accomplishments include the first formal release of the NPSS object-oriented architecture (NPSS Version 1) and the demonstration of a one order of magnitude reduction in computing cost-to-performance ratio using a cluster of personal computers. The paper also describes the future NPSS milestones, which include the simulation of space transportation propulsion systems in response to increased emphasis on safe, low cost access to space within NASA's Aerospace Technology Enterprise. In addition, the paper contains a summary of the feedback received from industry partners on the fiscal year 2000 effort and the actions taken over the past year to respond to that feedback. NPSS was supported in fiscal year 2001 by the High Performance Computing and Communications Program.

Lytle, John↗
NASA NTRS2002

Numerical Study of a Convective Turbulence Encounter

A numerical simulation of a convective turbulence event is investigated and compared with observational data. The specific case was encountered during one of NASA's flight tests and was characterized by severe turbulence. The event was associated with overshooting convective turrets that contained low to moderate radar reflectivity. Model comparisons with observations are quite favorable. Turbulence hazard metrics are proposed and applied to the numerical data set. Issues such as adequate grid size are examined.

Proctor, Fred H.↗
NASA NTRS2002

On the Numerical Convergence to Steady State of Hypersonic Flows Over Bodies with Concavities

Two recent numerical studies of hypersonic flows over bodies with concavities revealed problems with convergence to a steady state with an oft-used application of local-time-stepping. Both simulated flows showed a time-like, periodic shedding of vortices in a subsonic domain bounded by supersonic external flow although the simulations, using local-time-stepping, were not time accurate. Simple modifications to the numerical algorithm were implemented to enable implicit, first-order accurate in time simulations. Subsequent time-accurate simulations of the two test problems converged to a steady state. The baseline algorithm and modifications for temporal accuracy are described. The requirement for sub-iterations to achieve convergence is demonstrated. Failure to achieve convergence without time accuracy is conjectured to arise from temporal errors being continuously refocused into a subsonic domain.

Gnoffo, Peter A.↗
NASA NTRS2002

The Delta x B = 0 Constraint Versus Minimization of Numerical Errors in MHD Simulations

The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. It has previously been shown by Powell et al. (1995) that an 'almost' equivalent MHD system in non-conservative form can be derived. This non-conservative system has a better conditioned eigensystem. Aside from Powell et al., the MHD equations can be derived from basic principles in either conservative or non-conservative form. The Delta x B = 0 constraint of the MHD equations is only an initial condition constraint, it is very different from the incompressible Navier-Stokes equations in which the divergence condition is needed to close the system (i.e., to have the same number of equations and the same number of unknown). In the MHD formulations, if Delta x B = 0 initially, all one needs is to construct appropriate numerical schemes that preserve this constraint at later time evolutions. In other words, one does not need the Delta x B condition to close the MHD system. We formulate our new scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the divergence of the magnetic condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.

Yee, H. C.↗
NASA NTRS2002

Numerical Simulation of a Convective Turbulence Encounter

A numerical simulation of a convective turbulence event is investigated and compared with observational data. The numerical results show severe turbulence of similar scale and intensity to that encountered during the test flight. This turbulence is associated with buoyant plumes that penetrate the upper-level thunderstorm outflow. The simulated radar reflectivity compares well with that obtained from the aircraft's onboard radar. Resolved scales of motion as small as 50 m are needed in order to accurately diagnose aircraft normal load accelerations. Given this requirement, realistic turbulence fields may be created by merging subgrid-scales of turbulence to a convective-cloud simulation. A hazard algorithm for use with model data sets is demonstrated. The algorithm diagnoses the RMS normal loads from second moments of the vertical velocity field and is independent of aircraft motion.

Proctor, Fred H.↗
NASA NTRS2001

Evaluation of Sulfur Flow Emplacement on Io from Galileo Data and Numerical Modeling

Galileo images of bright lava flows surrounding Emakong Patera have been analyzed and numerical modeling has been performed to assess whether these flows could have resulted from the emplacement of sulfur lavas on Io. Images from the solid-state imaging.(SSI) camera show that these bright, white to yellow Emakong flows are up to 370 km long and contain dark, sinuous features that are interpreted to be lava conduits, approx. 300-500 m wide and > 100 km long. Near-Infrared Mapping Spectrometer (NIMS) thermal emission data yield a color temperature estimate of 344 K +/- 60 K (less than or equal to 131 C) within the Emakong caldera. We suggest that these bright flows likely resulted from either sulfur lavas or silicate lavas that have undergone extensive cooling, pyroclastic mantling, and/or alteration with bright sulfurous materials. The Emakong bright flows have estimated volumes of approx. 250-350 cu km, similar to some of the smaller Columbia River Basalt flows. If the Emakong flows did result from effusive sulfur eruptions, then they are orders of magnitude greater in volume than any terrestrial sulfur flows. Our numerical modeling results show that sulfur lavas on Io could have been emplaced as turbulent flows, which were capable of traveling tens to hundreds of kilometers, consistent with the predictions of Sagan [ 19793 and Fink et al. [ 19831. Our modeled flow distances are also consistent with the measured lengths of the Emakong channels and bright flows. Modeled thermal erosion rates are approx. 1-4 m/d for flows erupted at approx. 140-180 C, which are consistent with the melting rates of Kieffer et al. [2000]. The Emakong channels could be thermal erosional in nature; however, the morphologic signatures of thermal erosion channels cannot be discerned from available images. There are planned Galileo flybys of Io in 2001 which provide excellent opportunities to obtain high-resolution morphologic and color data of Emakong Patera. Such observations could, along with further modeling, provide additional information to better constrain whether sulfur lavas produced the Emakong flows.

Williams, David A.↗
NASA NTRS2003

Numerical Simulation of the Water Cycle Change Over the 20th Century

We have used numerical models to test the impact of the change in Sea Surface Temperatures (SSTs) and carbon dioxide (CO2) concentration on the global circulation, particularly focusing on the hydrologic cycle, namely the global cycling of water and continental recycling of water. We have run four numerical simulations using mean annual SST from the early part of the 20th century (1900-1920) and the later part (1980-2000). In addition, we vary the CO2 concentrations for these periods as well. The duration of the simulations is 15 years, and the spatial resolution is 2 degrees. We use passive tracers to study the geographical sources of water. Surface evaporation from predetermined continental and oceanic regions provides the source of water for each passive tracer. In this way, we compute the percent of precipitation of each region over the globe. This can also be used to estimate precipitation recycling. In addition, we are using the passive tracers to independently compute the global cycling of water (compared to the traditional, Q/P calculation).

Bosilovich, Michael G.↗
NASA NTRS2002

Libration Orbit Mission Design: Applications of Numerical & Dynamical Methods

Sun-Earth libration point orbits serve as excellent locations for scientific investigations. These orbits are often selected to minimize environmental disturbances and maximize observing efficiency. Trajectory design in support of libration orbits is ever more challenging as more complex missions are envisioned in the next decade. Trajectory design software must be further enabled to incorporate better understanding of the libration orbit solution space and thus improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple libration missions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes algorithm and software development. The recently launched Microwave Anisotropy Probe (MAP) and upcoming James Webb Space Telescope (JWST) and Constellation-X missions are examples of the use of improved numerical methods for attaining constrained orbital parameters and controlling their dynamical evolution at the collinear libration points. This paper presents a history of libration point missions, a brief description of the numerical and dynamical design techniques including software used, and a sample of future GSFC mission designs.

Bauer, Frank↗
NASA NTRS2002

The Impact of TRMM Data on Numerical Forecast of Mesoscale Systems

The impact of surface rainfall data derived from the TRMM Microwave Image (TMI) on the numerical forecast of mesoscale systems is evaluated. A series of numerical experiments are performed that assimilate TMI rainfall data into the Penn State University/National Centers for Atmospheric Research (PSU/NCAR) Mesoscale Model version 5 (MM5) using a four-dimensional variational data assimilation (4DVAR) technique. Experiments are conducted incorporating TMI rainfall data into the mesoscale model to improve hurricane initialization. It is found that assimilation of rainfall data into the model is beneficial in producing a more realistic eye and rain bands and also helps to improve the intensity forecast for the hurricane. Further 4DVAR experiments are performed on mesoscale convective systems (MCSs). Detailed results and related issues will be presented during the conference.

Pu, Zhao-Xia↗
NASA NTRS2003

Prospect of Using Numerical Dynamo Model for Prediction of Geomagnetic Secular Variation

Modeling of the Earth's core has reached a level of maturity to where the incorporation of observations into the simulations through data assimilation has become feasible. Data assimilation is a method by which observations of a system are combined with a model output (or forecast) to obtain a best guess of the state of the system, called the analysis. The analysis is then used as an initial condition for the next forecast. By doing assimilation, not only we shall be able to predict partially secular variation of the core field, we could also use observations to further our understanding of dynamical states in the Earth's core. One of the first steps in the development of an assimilation system is a comparison between the observations and the model solution. The highly turbulent nature of core dynamics, along with the absence of any regular external forcing and constraint (which occurs in atmospheric dynamics, for example) means that short time comparisons (approx. 1000 years) cannot be made between model and observations. In order to make sensible comparisons, a direct insertion assimilation method has been implemented. In this approach, magnetic field observations at the Earth's surface have been substituted into the numerical model, such that the ratio of the multiple components and the dipole component from observation is adjusted at the core-mantle boundary and extended to the interior of the core, while the total magnetic energy remains unchanged. This adjusted magnetic field is then used as the initial field for a new simulation. In this way, a time tugged simulation is created which can then be compared directly with observations. We present numerical solutions with and without data insertion and discuss their implications for the development of a more rigorous assimilation system.

Kuang, Weijia↗
NASA NTRS2003

Numerical Simulation of One- and Two-Phase Flows in Propulsion Systems

Four subprojects were conducted using analytical methods, numerical simulation and experimental tests: (A) Shock wave mitigation by spike-shaped blunt bodies with application for the purpose of drag, lift and longitudinal momentum optimization. The main result in this subproject is: application of a single needle against a supersonic flow provides higher benefits for blunt body drag reduction and heat transfer to the body than the application of multiple needles. (B) Solid particles, liquid and air jet injection through the front of a blunt body against a supersonic flow. In this case, the research conducted and analysis of multiple previous investigations in this area have shown essential benefits and preferable application of solid particle injection. (C) Comparison of different methods of fuel injection into supersonic duct flows. Preliminary numerical simulations and theoretical analysis show promising results for Telescope-shaped inlet applications in SCRAMJET; and (D) Development of an acoustic source location method for different applications including propulsion systems.

Gilinsky, Mikhail↗

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