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NASA NTRS2007

Analytic Formulation and Numerical Implementation of an Acoustic Pressure Gradient Prediction

The scattering of rotor noise is an area that has received little attention over the years, yet the limited work that has been done has shown that both the directivity and intensity of the acoustic field may be significantly modified by the presence of scattering bodies. One of the inputs needed to compute the scattered acoustic field is the acoustic pressure gradient on a scattering surface. Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. These formulations are presented in this paper. The first formulation is derived by taking the gradient of Farassat's retarded-time Formulation 1A. Although this formulation is relatively simple, it requires numerical time differentiation of the acoustic integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. The acoustic pressure gradient predicted by these new formulations is validated through comparison with the acoustic pressure gradient determined by a purely numerical approach for two model rotors. The agreement between analytic formulations and numerical method is excellent for both stationary and moving observers case.

Lee, Seongkyu↗
NASA NTRS2007

Toward Scientific Numerical Modeling

Ultimately, scientific numerical models need quantified output uncertainties so that modeling can evolve to better match reality. Documenting model input uncertainties and verifying that numerical models are translated into code correctly, however, are necessary first steps toward that goal. Without known input parameter uncertainties, model sensitivities are all one can determine, and without code verification, output uncertainties are simply not reliable. To address these two shortcomings, two proposals are offered: (1) an unobtrusive mechanism to document input parameter uncertainties in situ and (2) an adaptation of the Scientific Method to numerical model development and deployment. Because these two steps require changes in the computational simulation community to bear fruit, they are presented in terms of the Beckhard-Harris-Gleicher change model.

Kleb, Bil↗
NASA NTRS2008

An Experimental and Numerical Study of a Supersonic Burner for CFD Model Development

A laboratory scale supersonic burner has been developed for validation of computational fluid dynamics models. Detailed numerical simulations were performed for the flow inside the combustor, and coupled with finite element thermal analysis to obtain more accurate outflow conditions. A database of nozzle exit profiles for a wide range of conditions of interest was generated to be used as boundary conditions for simulation of the external jet, or for validation of non-intrusive measurement techniques. A set of experiments was performed to validate the numerical results. In particular, temperature measurements obtained by using an infrared camera show that the computed heat transfer was larger than the measured value. Relaminarization in the convergent part of the nozzle was found to be responsible for this discrepancy, and further numerical simulations sustained this conclusion.

Magnotti, G.↗
NASA NTRS2007

Binary Black Holes, Gravitational Waves, and Numerical Relativity

This viewgraph presentation reviews the massive black hole (MBH) binaries that are found at the center of most galaxies, "astronomical messenger", gravitational waves (GW), and the use of numerical relativity understand the features of these phenomena. The final merger of two black holes releases a tremendous amount of energy and is one of the brightest sources in the gravitational wave sky. Observing these sources with gravitational wave detectors requires that we know the radiation waveforms they emit. Since these mergers take place in regions of very strong gravitational fields, we need to solve Einstein's equations of general relativity on a computer in order to calculate these waveforms. For more than 30 years, scientists have tried to compute these waveforms using the methods of numerical relativity.. This talk will take you on this quest for the holy grail of numerical relativity, showing how a spacetime is constructed on a computer to build a simulation laboratory for binary black hole mergers. We will focus on the recent advances that are revealing these waveforms, and the dramatic new potential for discoveries that arises when these sources will be observed by LIGO and LISA.

Centrella, Joan↗
NASA NTRS2008

Analytic Formulation and Numerical Implementation of an Acoustic Pressure Gradient Prediction

Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. The pressure gradient can be used to solve the boundary condition for scattering problems and it is a key aspect to solve acoustic scattering problems. The first formulation is derived from the gradient of the Ffowcs Williams-Hawkings (FW-H) equation. This formulation has a form involving the observer time differentiation outside the integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. This formulation avoids the numerical time differentiation with respect to the observer time, which is computationally more efficient. The acoustic pressure gradient predicted by these new formulations is validated through comparison with available exact solutions for a stationary and moving monopole sources. The agreement between the predictions and exact solutions is excellent. The formulations are applied to the rotor noise problems for two model rotors. A purely numerical approach is compared with the analytical formulations. The agreement between the analytical formulations and the numerical method is excellent for both stationary and moving observer cases.

Lee, Seongkyu↗
NASA NTRS2009

Simulation of the Impact of New Aircraft- and Satellite-Based Ocean Surface Wind Measurements on H*Wind Analyses and Numerical Forecasts

The Hurricane Imaging Radiometer (HIRAD) is a new airborne microwave remote sensor for hurricane observations that is currently under development by NASA Marshall Space Flight Center, NOAA Hurricane Research Division, the University of Central Florida and the University of Michigan. HIRAD is being designed to enhance the realtime airborne ocean surface winds observation capabilities of NOAA and USAF Weather Squadron hurricane hunter aircraft using the operational airborne Stepped Frequency Microwave Radiometer (SFMR). Unlike SFMR, which measures wind speed and rain rate along the ground track directly beneath the aircraft, HIRAD will provide images of the surface wind and rain field over a wide swath (~ 3 x the aircraft altitude). The present paper describes a set of Observing System Simulation Experiments (OSSEs) in which measurements from the new instrument as well as those from existing instruments (air, surface, and space-based) are simulated from the output of a detailed numerical model, and those results are used to construct H*Wind analyses. The H*Wind analysis, a product of the Hurricane Research Division of NOAA s Atlantic Oceanographic and Meteorological Laboratory, brings together wind measurements from a variety of observation platforms into an objective analysis of the distribution of wind speeds in a tropical cyclone. This product is designed to improve understanding of the extent and strength of the wind field, and to improve the assessment of hurricane intensity. See http://www.aoml.noaa.gov/hrd/data_sub/wind.html. Evaluations will be presented on the impact of the HIRAD instrument on H*Wind analyses, both in terms of adding it to the full suite of current measurements, as well as using it to replace instrument(s) that may not be functioning at the future time the HIRAD instrument is implemented. Also shown will be preliminary results of numerical weather prediction OSSEs in which the impact of the addition of HIRAD observations to the initial state on numerical forecasts of the hurricane intensity and structure is assessed.

Miller, Timothy↗
NASA NTRS2007

Fusing Symbolic and Numerical Diagnostic Computations

X-2000 Anomaly Detection Language denotes a developmental computing language, and the software that establishes and utilizes the language, for fusing two diagnostic computer programs, one implementing a numerical analysis method, the other implementing a symbolic analysis method into a unified event-based decision analysis software system for realtime detection of events (e.g., failures) in a spacecraft, aircraft, or other complex engineering system. The numerical analysis method is performed by beacon-based exception analysis for multi-missions (BEAMs), which has been discussed in several previous NASA Tech Briefs articles. The symbolic analysis method is, more specifically, an artificial-intelligence method of the knowledge-based, inference engine type, and its implementation is exemplified by the Spacecraft Health Inference Engine (SHINE) software. The goal in developing the capability to fuse numerical and symbolic diagnostic components is to increase the depth of analysis beyond that previously attainable, thereby increasing the degree of confidence in the computed results. In practical terms, the sought improvement is to enable detection of all or most events, with no or few false alarms.

James, Mark↗
NASA NTRS2010

Simulation of the Impact of New Aircraft-and Satellite-based Ocean Surface Wind Measurements on Wind Analyses and Numerical Forecasts

The Hurricane Imaging Radiometer (HIRAD) is a new airborne microwave remote sensor for hurricane observations that is currently under development by NASA Marshall Space Flight Center, NOAA Hurricane Research Division, the University of Central Florida and the University of Michigan. HIRAD is being designed to enhance the realtime airborne ocean surface winds observation capabilities of NOAA and USAF Weather Squadron hurricane hunter aircraft currently using the operational airborne Stepped Frequency Microwave Radiometer (SFMR). Unlike SFMR, which measures wind speed and rain rate along the ground track directly beneath the aircraft, HIRAD will provide images of the surface wind and rain field over a wide swath (approx. 3 x the aircraft altitude). The present paper describes a set of Observing System Simulation Experiments (OSSEs) in which measurements from the new instrument as well as those from existing instruments (air, surface, and space-based) are simulated from the output of a detailed numerical model, and those results are used to construct H*Wind analyses, a product of the Hurricane Research Division of NOAA s Atlantic Oceanographic and Meteorological Laboratory. Evaluations will be presented on the impact of the HIRAD instrument on H*Wind analyses, both in terms of adding it to the full suite of current measurements, as well as using it to replace instrument(s) that may not be functioning at the future time the HIRAD instrument is implemented. Also shown will be preliminary results of numerical weather prediction OSSEs in which the impact of the addition of HIRAD observations to the initial state on numerical forecasts of the hurricane intensity and structure is assessed.

Miller, TImothy↗
NASA NTRS2011

Numerical Investigation of Rotorcraft Fuselage Drag Reduction Using Active Flow Control

The effectiveness of unsteady zero-net-mass-flux jets for fuselage drag reduction was evaluated numerically on a generic rotorcraft fuselage in forward flight with a rotor. Previous efforts have shown significant fuselage drag reduction using flow control for an isolated fuselage by experiment and numerical simulation. This work will evaluate a flow control strategy, that was originally developed on an isolated fuselage, in a more relevant environment that includes the effects of a rotor. Evaluation of different slot heights and jet velocity ratios were performed. Direct comparisons between an isolated fuselage and rotor/fuselage simulations were made showing similar flow control performance at a -3deg fuselage angle-of-attack condition. However, this was not the case for a -5deg angle-of-attack condition where the performance between the isolated fuselage and rotor/fuselage were different. The fuselage flow control resulted in a 17% drag reduction for a peak C(sub mu) of 0.0069 in a forward flight simulation where mu = 0:35 and CT/sigma = 0:08. The CFD flow control results also predicted a favorable 22% reduction of the fuselage download at this same condition, which can have beneficial compounding effects on the overall performance of the vehicle. This numerical investigation was performed in order to provide guidance for a future 1/3 scale wind tunnel experiment to be performed at the NASA 14-by 22-Foot Subsonic Tunnel.

Allan, Brian G.↗
NASA NTRS2011

Fast Numerical Methods for the Design of Layered Photonic Structures with Rough Interfaces

Modified boundary conditions (MBC) and a multilayer approach (MA) are proposed as fast and efficient numerical methods for the design of 1D photonic structures with rough interfaces. These methods are applicable for the structures, composed of materials with arbitrary permittivity tensor. MBC and MA are numerically validated on different types of interface roughness and permittivities of the constituent materials. The proposed methods can be combined with the 4x4 scattering matrix method as a field solver and an evolutionary strategy as an optimizer. The resulted optimization procedure is fast, accurate, numerically stable and can be used to design structures for various applications.

Komarevskiy, Nikolay↗
NASA NTRS2011

Observational and Numerical Diagnostics of Galaxy Cluster Outer Regions

Aims. We present the analysis of a local (z = 0.04 - 0.2) sample of 31 galaxy clusters with the aim of measuring the density of the X-ray emitting gas in cluster outskirts. We compare our results with numerical simulations to set constraints on the azimuthal symmetry and gas clumping in the outer regions of galaxy clusters. Methods. We exploit the large field-of-view and low instrumental background of ROSAT/PSPC to trace the density of the intracluster gas out to the virial radius. We perform a stacking of the density profiles to detect a signal beyond r(sub 200) and measure the typical density and scatter in cluster outskirts. We also compute the azimuthal scatter of the profiles with respect to the mean value to look for deviations from spherical symmetry. Finally, we compare our average density and scatter profiles with the results of numerical simulations. Results. As opposed to several recent results, we observe a steepening of the density profiles beyond approximately 0.3r(sub 500). Comparing our density profiles with simulations, we find that non-radiative runs predict too steep density profiles, whereas runs including additional physics and/or gas clumping are in better agreement with the observed gas distribution. We note a systematic difference between cool-core and non-cool core clusters beyond approximately 0.3r(sub 200), which we explain by a different distribution of the gas in the two classes. Beyond approximately r(sub 500), galaxy clusters deviate significantly from spherical symmetry, with only little differences between relaxed and disturbed systems. We find good agreement between the observed and predicted scatter profiles, but only when the 1% densest clumps are filtered out in the simulations. Conclusions. The general trend of steepening density around the virial radius indicates that the shallow density profiles found in several recent works were probably obtained along particular directions (e.g., filaments) and are not representative of the typical behavior of clusters. Comparing our results with numerical simulations, we find that non-radiative simulations fail to reproduce the gas distribution, even well outside cluster cores. Therefore, a detailed treatment of gas cooling, star formation, clumping, and AGN feedback is required to construct realistic models of cluster outer regions.

Eckert, D.↗
NASA NTRS2011

Numerically Exact Computer Simulations of Light Scattering by Densely Packed, Random Particulate Media

Direct computer simulations of electromagnetic scattering by discrete random media have become an active area of research. In this progress review, we summarize and analyze our main results obtained by means of numerically exact computer solutions of the macroscopic Maxwell equations. We consider finite scattering volumes with size parameters in the range, composed of varying numbers of randomly distributed particles with different refractive indices. The main objective of our analysis is to examine whether all backscattering effects predicted by the low-density theory of coherent backscattering (CB) also take place in the case of densely packed media. Based on our extensive numerical data we arrive at the following conclusions: (i) all backscattering effects predicted by the asymptotic theory of CB can also take place in the case of densely packed media; (ii) in the case of very large particle packing density, scattering characteristics of discrete random media can exhibit behavior not predicted by the low-density theories of CB and radiative transfer; (iii) increasing the absorptivity of the constituent particles can either enhance or suppress typical manifestations of CB depending on the particle packing density and the real part of the refractive index. Our numerical data strongly suggest that spectacular backscattering effects identified in laboratory experiments and observed for a class of high-albedo Solar System objects are caused by CB.

Dlugach, Janna M.↗
NASA NTRS2013

Verification of Numerical Programs: From Real Numbers to Floating Point Numbers

Numerical algorithms lie at the heart of many safety-critical aerospace systems. The complexity and hybrid nature of these systems often requires the use of interactive theorem provers to verify that these algorithms are logically correct. Usually, proofs involving numerical computations are conducted in the infinitely precise realm of the field of real numbers. However, numerical computations in these algorithms are often implemented using floating point numbers. The use of a finite representation of real numbers introduces uncertainties as to whether the properties veri ed in the theoretical setting hold in practice. This short paper describes work in progress aimed at addressing these concerns. Given a formally proven algorithm, written in the Program Verification System (PVS), the Frama-C suite of tools is used to identify sufficient conditions and verify that under such conditions the rounding errors arising in a C implementation of the algorithm do not affect its correctness. The technique is illustrated using an algorithm for detecting loss of separation among aircraft.

Goodloe, Alwyn E.↗
NASA NTRS2013

Numerical Modeling of Ablation Heat Transfer

A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.

Ewing, Mark E.↗
NASA NTRS2015

Numerical Computation of a Continuous-thrust State Transition Matrix Incorporating Accurate Hardware and Ephemeris Models

A significant body of work exists showing that providing a nonlinear programming (NLP) solver with expressions for the problem constraint gradient substantially increases the speed of program execution and can also improve the robustness of convergence, especially for local optimizers. Calculation of these derivatives is often accomplished through the computation of spacecraft's state transition matrix (STM). If the two-body gravitational model is employed as is often done in the context of preliminary design, closed form expressions for these derivatives may be provided. If a high fidelity dynamics model, that might include perturbing forces such as the gravitational effect from multiple third bodies and solar radiation pressure is used then these STM's must be computed numerically. We present a method for the power hardward model and a full ephemeris model. An adaptive-step embedded eight order Dormand-Prince numerical integrator is discussed and a method for the computation of the time of flight derivatives in this framework is presented. The use of these numerically calculated derivatieves offer a substantial improvement over finite differencing in the context of a global optimizer. Specifically the inclusion of these STM's into the low thrust missiondesign tool chain in use at NASA Goddard Spaceflight Center allows for an increased preliminary mission design cadence.

Low Thrust↗
NASA NTRS2013

Discrete Kinetic Eigenmode Spectra of Electron Plasma Oscillations in Weakly Collisional Plasma: A Numerical Study

It has been demonstrated that in the presence of weak collisions, described by the Lenard-Bernstein collision operator, the Landau-damped solutions become true eigenmodes of the system and constitute a complete set. We present numerical results from an Eulerian Vlasov code that incorporates the Lenard-Bernstein collision operator. The effect of the collisions on the numerical recursion phenomenon seen in Vlasov codes is discussed. The code is benchmarked against exact linear eigenmode solutions in the presence of weak collisions, and a spectrum of Landau-damped solutions is determined within the limits of numerical resolution. Tests of the orthogonality and the completeness relation are presented.

Kinetic Eigenmode Spectra↗
NASA NTRS2009

Mean Element Propagations Using Numerical Averaging

The long-term evolution characteristics (and stability) of an orbit are best characterized using a mean element propagation of the perturbed two body variational equations of motion. The averaging process eliminates short period terms leaving only secular and long period effects. In this study, a non-traditional approach is taken that averages the variational equations using adaptive numerical techniques and then numerically integrating the resulting EOMs. Doing this avoids the Fourier series expansions and truncations required by the traditional analytic methods. The resultant numerical techniques can be easily adapted to propagations at most solar system bodies.

orbit propagations↗
NASA NTRS1994

Numerical and Experimental Study of Transport Phenomena in Directional Solidification of Succinonitrile

A numerical and experimental study of the growth of succinonitrile (SCN) using a horizontal Bridginan furnace and transparent glass ampoule was conducted. Two experiments were considered: one in which the temperature profile was fixed relative to the ampoule (no-growth case); and a second in which the thermal profile was translated at a constant rate (steady growth case). Measured temperature profiles on the outer surface of the ampoule were used as thermal boundary conditions for the modelling. The apparent heat capacity formulation combined with the variable viscositymeth~ was used to model the phase change in SeN. Both 2-D and 3-D models were studied and numerical solutions obtained using the commercial finite element code, FIDAP1. Comparison of the numerical results to experimental data showed excellent agreement. The complex 3-D shallow-cavity flow in the melt, differences between 2-D and 3-D models, effects of natural convection on the thermal gradient and shape of the solid/liquid interface, and the sensitivity of simulations to specific assumptions, are also discussed.

de Groh, Henry C., III↗