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NASA NTRS1992

Computing interface motion in compressible gas dynamics

An analysis is conducted of the coupling of Osher and Sethian's (1988) 'Hamilton-Jacobi' level set formulation of the equations of motion for propagating interfaces to a system of conservation laws for compressible gas dynamics, giving attention to both the conservative and nonconservative differencing of the level set function. The capabilities of the method are illustrated in view of the results of numerical convergence studies of the compressible Rayleigh-Taylor and Kelvin-Helmholtz instabilities for air-air and air-helium boundaries.

Mulder, W.↗

NASA NTRS1984

Simplified combustion noise theory yielding a prediction of fluctuating pressure level

The first order equations for the conservation of mass and momentum in differential form are combined for an ideal gas to yield a single second order partial differential equation in one dimension and time. Small perturbation analysis is applied. A Fourier transformation is performed that results in a second order, constant coefficient, nonhomogeneous equation. The driving function is taken to be the source of combustion noise. A simplified model describing the energy addition via the combustion process gives the required source information for substitution in the driving function. This enables the particular integral solution of the nonhomogeneous equation to be found. This solution multiplied by the acoustic pressure efficiency predicts the acoustic pressure spectrum measured in turbine engine combustors. The prediction was compared with the overall sound pressure levels measured in a CF6-50 turbofan engine combustor and found to be in excellent agreement.

Huff, R. G.↗

NASA NTRS2021

Importance of Quantifying the Full-depth Carbon Reservoir of Jamaica Bay Salt Marshes, New York

Constraining uncertainty in the global carbon cycle requires valid assessment of both surface and stored carbon in marine and coastal ecosystems (Blue Carbon) as well as terrestrial carbon (forests, peatlands, and soils) [Pendleton et al., 2012]. Quantifying the global carbon stock of coastal salt marshes, potentially the most efficient carbon-burying ecosystems in the world per area, is a key area of further research in both of these fields Pendleton et al., 2012. One of the largest challenges is that despite the fact that salt marshes often sequester carbon several meters deep, nearly all estimates of salt marsh carbon stocks consider only the upper 1 m of sediment (Windham-Myers et al., 2015) [54]. This is particularly concerning because coastal wetlands are increasingly at risk due to climate change, sea level rise, and anthropogenic disturbance and destruction (Deegan et al., 2012) [15]. Using full-depth measurements from marsh cores, we estimate the carbon stock of five salt marshes in the highly urbanized estuary of Jamaica Bay, New York and argue that partial-depth measurements can underestimate carbon stocks. These estimates use calculated carbon content and probe depth data of these marshes collected between 2000 and 2019, applying this data across the full area of the marsh obtained from satellite imagery. Carbon density measurements are then multiplied by the full-depth volume of the marshes to create an estimate of total carbon stock. In addition to calculating present-day estimates, we compare our carbon stock estimates to historical Jamaica Bay imagery to calculate historical carbon stocks and carbon loss. The carbon stock estimates presented here show a 95% carbon stock loss between 1885 and 2019 in Jamaica Bay and highlight the severe underestimation of carbon stocks without full-depth calculations. These findings have important implications for disappearing salt marshes with regard to the global carbon cycle and the incorporation of belowground carbon into global climate models. The findings are increasingly relevant for advocacy efforts aiming to conserve these marshes with sea level rise.

Tidal wetlands↗

NASA NTRS1997

Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the Hamilton-Jacobi (H-J), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the H-J equations. Unfortunately, the basic scheme lacks proper Lipschitz continuity of the numerical Hamiltonian. By employing a virtual edge flipping technique, Lipschitz continuity of the numerical flux is restored on acute triangulations. Next, schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous Hamiltonians. These schemes possess a discrete maximum principle on arbitrary triangulations and naturally exhibit proper Lipschitz continuity of the numerical Hamiltonian. Finally, a class of Petrov-Galerkin approximations are considered. These schemes are stabilized via a least-squares bilinear form. The Petrov-Galerkin schemes do not possess a discrete maximum principle but generalize to high order accuracy.

Barth, Timothy J.↗

NASA NTRS1975

An assessment of the benefits of the use of NASA developed fuel conservative technology in the US commercial aircraft fleet

Cost and benefits of a fuel conservative aircraft technology program proposed by NASA are estimated. NASA defined six separate technology elements for the proposed program: (a) engine component improvement (b) composite structures (c) turboprops (d) laminar flow control (e) fuel conservative engine and (f) fuel conservative transport. There were two levels postulated: The baseline program was estimated to cost $490 million over 10 years with peak funding in 1980. The level two program was estimated to cost an additional $180 million also over 10 years. Discussions with NASA and with representatives of the major commercial airframe manufacturers were held to estimate the combinations of the technology elements most likely to be implemented, the potential fuel savings from each combination, and reasonable dates for incorporation of these new aircraft into the fleet.

Source record↗

NASA NTRS1979

Lyman-alpha rocket spectra and models of the quiet and active solar chromosphere based on partial redistribution diagnostics

Absolute intensity Lyman-alpha profiles with a spatial resolution of 0.8 min and a spectral resolution of 50 mA were obtained for network and cell regions in the quiet sun, umbral and penumbral areas of a sunspot, two plages, and a quiescent prominence of the limb. Weak limb brightening shown by the Lyman-alpha cores and wings are consistent with predictions derived from partial redistribution line transfer calculations. Through use of a comoving two-level partial redistribution code which conserves mass flux, unequal red and blue Lyman-alpha peak intensities may be interpreted as flow velocities near 20,000 K. Outflows in the plages and downflows in the network are also noted. A model of a mean quiet sun chromosphere consistent with the Lyman-alpha integrated intensity, the Lyman continuum slope, and the millimeter continuum is presented.

Basri, G. S.↗

NASA NTRS2003

International Space Station Microgravity Analytical Model Correlation And Update

The acceleration environment aboard the completed International Space Station (ISS) is a key resource for scientific and technological endeavors. Hardware verification activIties and early measurements indicate that the ISS is well on the way of meeting these "Assembly Complete" "microgravity" provisions, however, the simulation models that compute these accelerations have, to date, lacked the high degree of empirical validation typical of standard aerospace industry practices. Assembly stage, on-orbit measurements are used to address this shortcoming and to develop higher confidence in the simulation models. The Phase I correlation results show the analyses to be consistently conservative, producing higher than measured levels. The 25 to 30% greater quasi-steady computations are deemed acceptable for verification. Updates are made to localized structural dynamic and vibroacoustic parameters that reduce responses in selected one-third octave bands by almost 50%. These models are then used for the Assembly Complete verification analysis which concludes that the ISS vehicle meets the ISS microgravity requirements with minor reservations. Two of the sixteen rack are marginally non-compliant in the quasi-steady regime, and operational constraints are needed on the U. S. Lab and ESA APM vacuum resource vents, and the Russian Resistive Exercise Device in the structural dynamic regime.

DelBasso, Steve↗

NASA NTRS1984

Second- and third-order upwind difference schemes for hyperbolic conservation laws

Second- and third-order two time-level five-point explicit upwind-difference schemes are described for the numerical solution of hyperbolic systems of conservation laws and applied to the Euler equations of inviscid gas dynamics. Nonliner smoothing techniques are used to make the schemes total variation diminishing. In the method both hyperbolicity and conservation properties of the hyperbolic conservation laws are combined in a very natural way by introducing a normalized Jacobian matrix of the hyperbolic system. Entropy satisfying shock transition operators which are consistent with the upwind differencing are locally introduced when transonic shock transition is detected. Schemes thus constructed are suitable for shockcapturing calculations. The stability and the global order of accuracy of the proposed schemes are examined. Numerical experiments for the inviscid Burgers equation and the compressible Euler equations in one and two space dimensions involving various situations of aerodynamic interest are included and compared.

Yang, J. Y.↗

NASA NTRS1988

On the convergence of difference approximations to scalar conservation laws

A unified treatment is given for time-explicit, two-level, second-order-resolution (SOR), total-variation-diminishing (TVD) approximations to scalar conservation laws. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced to obtain results in terms of the latter. The existence of a cell entropy inequality is discussed, and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first-order accurate in general. Convergence for TVD-SOR schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.

Osher, Stanley↗

NASA NTRS1975

Design of short haul aircraft for fuel conservation

Current jet fuel prices of twice the 1972 level have significantly changed the characteristics of airplane design for best economy. The results of a contract with the NASA Ames Advanced Concepts and Missions Division confirmed the economic desirability of lower design cruise speeds and higher aspect-ratio wings compared to designs developed in the by-gone era of low fuel price. Evaluation of potential fuel conservation for short-haul aircraft showed that an interaction of airfoil technology and desirable engine characteristics is important: the supercritical airfoil permits higher aspect ratio wings with lower sweep; these, in turn, lower the cruise thrust requirements so that engines with higher bypass ratios are better matched in terms of lapse rate; lower cruise speeds (which are also better for fuel and operating cost economy) push the desired bypass ratio up further. Thus, if fuel prices remain high, or rise further, striking reductions in community noise level can be achieved as a fallout in development of a 1980s airplane and engine. Analyses are presented of developmental trends in the design of short-haul aircraft with lower cruise speeds and higher aspect-ratio wings, and the effects on fuel consumption of design field length, powered lift concepts, and turboprop as well as turbofan propulsion are discussed.

Bowden, M. K.↗

NASA NTRS2006

Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

Borrowing from techniques developed for conservation law equations, we have developed both monotone and higher order accurate numerical schemes which discretize the Hamilton-Jacobi and level set equations on triangulated domains. The use of unstructured meshes containing triangles (2D) and tetrahedra (3D) easily accommodates mesh adaptation to resolve disparate level set feature scales with a minimal number of solution unknowns. The minisymposium talk will discuss these algorithmic developments and present sample calculations using our adaptive triangulation algorithm applied to various moving interface problems such as etching, deposition, and curvature flow.

Barth, Timothy J.↗

NASA NTRS1998

Of mice and genes: evolution of vertebrate brain development

In this review the current understanding of genetic and molecular evolution of development, in particular the formation of the major axis of bilateral animals, is critically evaluated, and the early pattern formation in the hindbrain is related as much as possible to these processes. On the genetic level it is proposed that the exuberant multiplication of regulatory genes compared to that of structural genes relates to the increased flexibility of early vertebrate development. In comparisons to fruit flies, many conserved genes are found to be expressed very differently, while many others seem to reflect a comparable pattern and thus suggest a conservation of function. Even genes with a largely conserved pattern of expression may change the level at which they are expressed and the mechanisms by which they are regulated in their expression. Evolution and development of hindbrain motoneurons is reviewed, and it is concluded that both comparative data as well as more recent experimental data suggest a limited importance for the rhombomeres. Clearly, many cell fate-specifying processes work below the level of rhombomeres or in the absence of rhombomeres. It is suggested that more comparative developmental data are needed to establish firmly the relationship between homeobox genes and rhombomere specification in vertebrates other than a few model species.

NASA Discipline Developmental Biology↗

NASA NTRS1993

Recent advances in computational structural reliability analysis methods

The goal of structural reliability analysis is to determine the probability that the structure will adequately perform its intended function when operating under the given environmental conditions. Thus, the notion of reliability admits the possibility of failure. Given the fact that many different modes of failure are usually possible, achievement of this goal is a formidable task, especially for large, complex structural systems. The traditional (deterministic) design methodology attempts to assure reliability by the application of safety factors and conservative assumptions. However, the safety factor approach lacks a quantitative basis in that the level of reliability is never known and usually results in overly conservative designs because of compounding conservatisms. Furthermore, problem parameters that control the reliability are not identified, nor their importance evaluated. A summary of recent advances in computational structural reliability assessment is presented. A significant level of activity in the research and development community was seen recently, much of which was directed towards the prediction of failure probabilities for single mode failures. The focus is to present some early results and demonstrations of advanced reliability methods applied to structural system problems. This includes structures that can fail as a result of multiple component failures (e.g., a redundant truss), or structural components that may fail due to multiple interacting failure modes (e.g., excessive deflection, resonate vibration, or creep rupture). From these results, some observations and recommendations are made with regard to future research needs.

Thacker, Ben H.↗

NASA NTRS1986

Effect of subcooling on the on-orbit pressurization rate of cryogenic propellant tankage

The SOLA-ECLIPSE code is being developed to enable prediction of the behavior of cryogenic propellants in spacecraft tankage. A brief description of the formulations used for modeling heat transfer and for determining thermodynamic state is presented. Code performance is verified through comparison to experimental data for the self-pressurization of scale model liquid hydrogen tanks. SOLA-ECLIPSE is used to examine the effect of initial subcooling of the liquid phase on the self-pressurization rate of an on-orbit full scale liquid hydrogen tank typical for a chemical propulsion Orbital Transfer Vehicle. The computational predictions show that even small amounts of subcooling will significantly decrease the self-pressurization rate. Further, if the cooling is provided by a Thermodynamic Vent System, it is concluded that small levels of subcooling will maximize propellant conservation.

Hochstein, J. I.↗

NASA NTRS1989

Nonlinear filters for efficient shock computation

A new type of methods for the numerical approximation of hyperbolic conservation laws with discontinuous solution is introduced. The methods are based on standard finite difference schemes. The difference solution is processed with a nonlinear conservation form filter at every time level to eliminate spurious oscillations near shocks. It is proved that the filter can control the total variation of the solution and also produce sharp discrete shocks. The method is simpler and faster than many other high resolution schemes for shock calculations. Numerical examples in one and two space dimensions are presented.

Engquist, Bjorn↗

NASA NTRS1990

Prediction of self-pressurization rate of cryogenic propellant tankage

The SOLA-ECLIPSE code is being developed to enable prediction of the behavior of cryogenic propellants in spacecraft tankage. A brief description of the formulations used for modeling heat transfer and for determining the thermodynamic state is presented. Code performance is verified through comparison to experimental data for the self-pressurization of scale-model liquid hydrogen tanks. SOLA-ECLIPSE is used to examine the effect of initial subcooling of the liquid phase on the self-pressurization rate of an on-orbit full-scale liquid hydrogen tank typical for a chemical-propulsion orbit transfer vehicle. The computational predictions show that even small amounts of subcooling will significantly decrease the self-pressurization rate. Further, if the cooling is provided by a thermodynamic vent system, it is concluded that small levels of subcooling will maximize propellant conservation.

Hochstein, John I.↗

NASA NTRS1981

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. II - Five-point schemes

This paper presents a family of two-level five-point implicit schemes for the solution of one-dimensional systems of hyperbolic conservation laws, which generalized the Crank-Nicholson scheme to fourth order accuracy (4-4) in both time and space. These 4-4 schemes are nondissipative and unconditionally stable. Special attention is given to the system of linear equations associated with these 4-4 implicit schemes. The regularity of this system is analyzed and efficiency of solution-algorithms is examined. A two-datum representation of these 4-4 implicit schemes brings about a compactification of the stencil to three mesh points at each time-level. This compact two-datum representation is particularly useful in deriving boundary treatments. Numerical results are presented to illustrate some properties of the proposed scheme.

Harten, A.↗

NASA NTRS2005

Advanced Small Perturbation Potential Flow Theory for Unsteady Aerodynamic and Aeroelastic Analyses

An advanced small perturbation (ASP) potential flow theory has been developed to improve upon the classical transonic small perturbation (TSP) theories that have been used in various computer codes. These computer codes are typically used for unsteady aerodynamic and aeroelastic analyses in the nonlinear transonic flight regime. The codes exploit the simplicity of stationary Cartesian meshes with the movement or deformation of the configuration under consideration incorporated into the solution algorithm through a planar surface boundary condition. The new ASP theory was developed methodically by first determining the essential elements required to produce full-potential-like solutions with a small perturbation approach on the requisite Cartesian grid. This level of accuracy required a higher-order streamwise mass flux and a mass conserving surface boundary condition. The ASP theory was further developed by determining the essential elements required to produce results that agreed well with Euler solutions. This level of accuracy required mass conserving entropy and vorticity effects, and second-order terms in the trailing wake boundary condition. Finally, an integral boundary layer procedure, applicable to both attached and shock-induced separated flows, was incorporated for viscous effects. The resulting ASP potential flow theory, including entropy, vorticity, and viscous effects, is shown to be mathematically more appropriate and computationally more accurate than the classical TSP theories. The formulaic details of the ASP theory are described fully and the improvements are demonstrated through careful comparisons with accepted alternative results and experimental data. The new theory has been used as the basis for a new computer code called ASP3D (Advanced Small Perturbation - 3D), which also is briefly described with representative results.

Batina, John T.↗