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NASA NTRS1984

On the instability of a 3-dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach

The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.

Hall, P.↗

NASA NTRS1987

The delineation and interpretation of the Earth's gravity field

The geoid and topographic fields of the central Pacific were delineated and shown to correlate closely at intermediate wavelengths (500 to 2500 km). The associated admittance shows that anomalies having wavelengths less than about 1000 km are probably supported by the elastic strength of the lithosphere. Larger wavelength anomalies are due to dynamic effects in the sublithosphere. Direct modeling of small scale convection in the asthenosphere shows that the amplitudes of observed geoid and topographic anomalies can be independently matched, but that the observed admittance cannot. Only by imposing an initial regional variation in the thermal regime is it possible to match the admittance. It is proposed that this variation may be due to differences in the onset time of convection beneath the lithosphere of different ages. That is, convection beneath thickening lithosphere is strongly dependent on the rate of thickening (V) relative to the rise time for convection. The critical Rayleigh number contains the length scale K/V, where K is thermal diffusivity. Young, fast growing lithosphere stabilizes the underlying asthenosphere unless it has an unusually low viscosity. Lithosphere of different age, separated by fracture zones, will go unstable at different times, producing regional horizontal temperature gradient that may strongly influence convection. Laboratory and numerical experiments are proposed to study this form of convection and its influence on the geoid.

Marsh, Bruce D.↗

NASA NTRS1988

Three legged walking mobile platform: Kinematic and dynamic analysis and simulation

The three legged walker is proposed as a mobile work platform for numerous tasks associated with lunar base site preparation and construction. It is seen as one of several forms of surface transportation, each of which will be best suited for its respective tasks. Utilizing the principle of dynamic stability and taking advantage of the Moon's gravity, it appears to be capable of walking in any radial direction and rotating about a point. Typical curved path walking could involve some combination of the radial and rotational movements. Comprised mainly of a body, six actuators, and six moving parts, it is mechanically quite simple. Each leg connects to the body at a hip joint and has a femur, a knee joint, and a tibia that terminates at a foot. Also capable of enabling or enhancing the dexterity of a series of implements, the walker concept provides a mechanically simple and weight efficient means of drilling, digging, mining, and transporting cargo, and performing other like tasks. A proof of principle machine demonstrated the feasibility of the walking concept.

Mcmurray, Gary V.↗

NASA NTRS1992

Fully nonlinear development of the most unstable goertler vortex in a three dimensional boundary layer

The nonlinear development is studied of the most unstable Gortler mode within a general 3-D boundary layer upon a suitably concave surface. The structure of this mode was first identified by Denier, Hall and Seddougui (1991) who demonstrated that the growth rate of this instability is O(G sup 3/5) where G is the Gortler number (taken to be large here), which is effectively a measure of the curvature of the surface. Previous researchers have described the fate of the most unstable mode within a 2-D boundary layer. Denier and Hall (1992) discussed the fully nonlinear development of the vortex in this case and showed that the nonlinearity causes a breakdown of the flow structure. The effect of crossflow and unsteadiness upon an infinitesimal unstable mode was elucidated by Bassom and Hall (1991). They demonstrated that crossflow tends to stabilize the most unstable Gortler mode, and for certain crossflow/frequency combinations the Gortler mode may be made neutrally stable. These vortex configurations naturally lend themselves to a weakly nonlinear stability analysis; work which is described in a previous article by the present author. Here we extend the ideas of Denier and Hall (1992) to the three-dimensional boundary layer problem. It is found that the numerical solution of the fully nonlinear equations is best conducted using a method which is essentially an adaption of that utilized by Denier and Hall (1992). The influence of crossflow and unsteadiness upon the breakdown of the flow is described.

Otto, S. R.↗

NASA NTRS1994

Gravitational instabilities in protostellar disks

The nonaxisymmetric stability of self-gravitating, geometrically thick accretion disks has been studied for protostellar systems having a wide range of disk-to-central object mass ratios. Global eigenmodes with four distinctly different characters were identified using numerical, nonlinear hydrodynamic techniques. The mode that appears most likely to arise in normal star formation settings, however, resembles the 'eccentric instability' that was identified earlier in thin, nearly Keplerian disks: It presents an open, one-armed spiral pattern that sweeps continuously in a trailing direction through more than 2-pi radians, smoothly connecting the inner and outer edges of the disk, and requires cooperative motion of the point mass for effective amplification. This particular instability promotes the development of a single, self-gravitating clump of material in orbit about the point mass, so its routine appearance in our simulations supports the conjecture that the eccentric instability provides a primary route to the formation of short-period binaries in protostellar systems.

Tohline, J. E.↗

NASA NTRS2003

Diabatic Initialization of Mesoscale Models in the Southeastern United States: Can 0 to 12h Warm Season QPF be Improved?

It is well known that numerical warm season quantitative precipitation forecasts lack significant skill for numerous reasons. Some are related to the model--it may lack physical processes required to realistically simulate convection or the numerical algorithms and dynamics employed may not be adequate. Others are related to initialization-mesoscale features play an important role in convective initialization and atmospheric observation systems are incapable of properly depicting the three-dimensional stability structure at the mesoscale. The purpose of this study is to determine if a mesoscale model initialized with a diabatic initialization scheme can improve short-term (0 to 12h) warm season quantitative precipitation forecasts in the Southeastern United States. The Local Analysis and Prediction System (LAPS) developed at the Forecast System Laboratory is used to diabatically initialize the Pennsylvania State University/National center for Atmospheric Research (PSUNCAR) Mesoscale Model version 5 (MM5). The SPORT Center runs LAPS operationally on an hourly cycle to produce analyses on a 15 km covering the eastern 2/3 of the United States. The 20 km National Centers for Environmental Prediction (NCEP) Rapid Update Cycle analyses are used for the background fields. Standard observational data are acquired from MADIS with GOES/CRAFT Nexrad data acquired from in-house feeds. The MM5 is configured on a 140 x 140 12 km grid centered on Huntsville Alabama. Preliminary results indicate that MM5 runs initialized with LAPS produce improved 6 and 12h QPF threat scores compared with those initialized with the NCEP RUC.

Lapenta, William M.↗

NASA NTRS2008

High-Order Energy Stable WENO Schemes

A new third-order Energy Stable Weighted Essentially NonOscillatory (ESWENO) finite difference scheme for scalar and vector linear hyperbolic equations with piecewise continuous initial conditions is developed. The new scheme is proven to be stable in the energy norm for both continuous and discontinuous solutions. In contrast to the existing high-resolution shock-capturing schemes, no assumption that the reconstruction should be total variation bounded (TVB) is explicitly required to prove stability of the new scheme. A rigorous truncation error analysis is presented showing that the accuracy of the 3rd-order ESWENO scheme is drastically improved if the tuning parameters of the weight functions satisfy certain criteria. Numerical results show that the new ESWENO scheme is stable and significantly outperforms the conventional third-order WENO finite difference scheme of Jiang and Shu in terms of accuracy, while providing essentially nonoscillatory solutions near strong discontinuities.

Yamaleev, Nail K.↗

NASA NTRS2010

Interaction Between the Celestial and the Terrestrial Reference Frames

Effects of International Celestial Reference Frame (ICRF2) on the Terrestrial Reference Frames (TRF), CRF and EOP's, The ICRF2 became official on Jan. 1, 2010. It includes positions of 3414 compact radio astronomical sources observed with VLBI, a fivefold increase from the first ICRF. Numerous new VLBI models were used and the most unstable sources were treated as arc parameters to avoid distortions of the frame. The ICRF2 has a noise floor of 40 micro-arc-seconds and an axis stability of 10 micro-arc-seconds. It was aligned with the ICRS using 138 stable sources common to ICRF2 and ICRF-Ext2. Maintenance of ICRF2 is to be made using 295 defining sources chosen for their historical positional stability, minimal source structure, and sky distribution. Their stability and their more uniform sky distribution eliminate the two largest weaknesses of ICRF I. The switchover to ICRF2 has some small effects on the TRF, CRF and Earth Orientation Parameters (EOP). A CRF based on ICRF2 shows a relative rotation of 40 micro-arc-seconds, mostly about the Y-axis. Small shifts are also seen in the EOP's, the largest being 11 micro-arc-seconds in X-pole. Some small but insignificant differences are also seen in the TRF. These results will be presented and discussed.

Gordon, David↗

NASA NTRS2016

Elevated Aerosol Layers and Their Radiative Impact over Kanpur During Monsoon Onset Period

Accurate information about aerosol vertical distribution is needed to reduce uncertainties in aerosol radiative forcing and its effect on atmospheric dynamics. The present study deals with synergistic analyses of aerosol vertical distribution and aerosol optical depth (AOD) with meteorological variables using multisatellite and ground-based remote sensors over Kanpur in central Indo-Gangetic Plain (IGP). Micro-Pulse Lidar Network-derived aerosol vertical extinction (sigma) profiles are analyzed to quantify the interannual and daytime variations during monsoon onset period (May-June) for 2009-2011. The mean aerosol profile is broadly categorized into two layers viz., a surface layer (SL) extending up to 1.5 km (where sigma decreased exponentially with height) and an elevated aerosol layer (EAL) extending between 1.5 and 5.5 km. The increase in total columnar aerosol loading is associated with relatively higher increase in contribution from EAL loading than that from SL. The mean contributions of EALs are about 60%, 51%, and 50% to total columnar AOD during 2009, 2010, and 2011, respectively. We observe distinct parabolic EALs during early morning and late evening but uniformly mixed EALs during midday. The interannual and daytime variations of EALs are mainly influenced by long-range transport and convective capacity of the local emissions, respectively. Radiative flux analysis shows that clear-sky incoming solar radiation at surface is reduced with increase in AOD, which indicates significant cooling at surface. Collocated analysis of atmospheric temperature and aerosol loading reveals that increase in AOD not only resulted in surface dimming but also reduced the temperature (approximately 2-3 C) of lower troposphere (below 3 km altitude). Radiative transfer simulations indicate that the reduction of incoming solar radiation at surface is mainly due to increased absorption by EALs (with increase in total AOD). The observed cooling in lower troposphere in high aerosol loading scenario could be understood as a dynamical feedback of EAL-induced stratification of lower troposphere. Further, the observed radiative effect of EALs increases the stability of the lower troposphere, which could modulate the large-scale atmospheric dynamics during monsoon onset period. These findings encourage follow-up studies on the implication of EALs to the Indian summer monsoon dynamics using numerical models.

aerosol vertical distribution↗

NASA NTRS1990

On the numerical simulation of spatial disturbances in blunt-nose flat plate flow

The feasibility of the simulation of the evolution of spatially amplified disturbances in realistic airfoil flows using a standard Navier-Stokes airfoil code is considered for a blunt-nose flat plate flow. A basic stationary flow and its linear-stability-theory characteristics are analyzed. A computational C-grid is generated using an algebraic grid-generation technique. It is concluded that further improvements to the computational grid and to the code are necessary to make the proposed simulations economical.

Laurien, Eckart↗

NASA NTRS1980

Stability of the stratifield cylindrical annulus flow

The linear stability analysis for the stratified flow between two rotating circular cylinders is formulated. Two approaches for the stability analysis are presented. The first approach results in an algebraic eigenvalue problem, while the second results in an initial value problem for the perturbation function. The advantages and disadvantages of both approaches are discussed and a preferable numerical solution technique is outlined.

Antar, B. N.↗

NASA NTRS1984

Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations

MacCormack's implicit finite-difference scheme was used to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method for solving the PNS equations does not require the inversion of block tridiagonal systems of algebraic equations and permits the original explicit MacCormack scheme to be employed in those regions where implicit treatment is not needed. The advantages and disadvantages of the present adaptation are discussed in relation to those of the conventional Beam-Warming scheme for a flat plate boundary layer test case. Comparisons are made for accuracy, stability, computer time, computer storage, and ease of implementation. The present method was also applied to a second test case of hypersonic laminar flow over a 15% compression corner. The computed results compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.

Lawrence, J. L.↗

NASA NTRS1985

Energy efficient transport technology: Program summary and bibliography

The Energy Efficient Transport (EET) Program began in 1976 as an element of the NASA Aircraft Energy Efficiency (ACEE) Program. The EET Program and the results of various applications of advanced aerodynamics and active controls technology (ACT) as applicable to future subsonic transport aircraft are discussed. Advanced aerodynamics research areas included high aspect ratio supercritical wings, winglets, advanced high lift devices, natural laminar flow airfoils, hybrid laminar flow control, nacelle aerodynamic and inertial loads, propulsion/airframe integration (e.g., long duct nacelles) and wing and empennage surface coatings. In depth analytical/trade studies, numerous wind tunnel tests, and several flight tests were conducted. Improved computational methodology was also developed. The active control functions considered were maneuver load control, gust load alleviation, flutter mode control, angle of attack limiting, and pitch augmented stability. Current and advanced active control laws were synthesized and alternative control system architectures were developed and analyzed. Integrated application and fly by wire implementation of the active control functions were design requirements in one major subprogram. Additional EET research included interdisciplinary technology applications, integrated energy management, handling qualities investigations, reliability calculations, and economic evaluations related to fuel savings and cost of ownership of the selected improvements.

Middleton, D. B.↗

NASA NTRS1986

Hierarchial implicit dynamic least-square solution algorithm

This paper develops an implicit type transient solution strategy which possesses hierarchial levels of application. In particular, due to the manner of formulation, stiffness updating, assembly inversion, solution constraint, as well as iteration are all performed at a localized level. The level of iterative calculations depends on the type of hierarchial partitioning employed, namely degree of freedom, nodal, elemental, material/nonlinear group, substructural, and so on. Since the iterative solution process and application of constraints are applied at a local level, the resulting so-called hierarchial implicit solution algorithm possesses very stable and efficient numerical properties and is highly storage efficient. To demonstrate the scheme, the results of several benchmark examples are presented. These enable comparisons with the Newton-Raphson solved implicit transient solution method. Overall the comparisons illustrate the superior stability and efficiency of the hierarchial scheme.

Padovan, J.↗

NASA NTRS1986

On the instability of a three-dimensional attachment-line boundary layer - Weakly nonlinear theory and a numerical approach

The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier-Stokes equations for the attachment-line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.

Hall, P.↗

NASA NTRS1989

A new uniformly valid asymptotic integration algorithm for elasto-plastic-creep and unified viscoplastic theories including continuum damage

A new scheme to integrate a system of stiff differential equations for both the elasto-plastic creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.

Chulya, A.↗

NASA NTRS1991

A new uniformly valid asymptotic integration algorithm for elasto-plastic creep and unified viscoplastic theories including continuum damage

Chulya, Abhisak↗

NASA NTRS1992

Thermomechanical buckling and postbuckling of multilayered composite panels

A study is made of the thermomechanical buckling and postbuckling responses of flat unstiffened composite panels. The panels are subjected to combined temperature change and applied edge displacement. The analysis is based on a first-order shear deformation, von Karman type nonlinear plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. An efficient multiple-parameter reduction method is used in conjunction with mixed finite element models, for determining the stability boundary and postbuckling response. The reduction method is also used for evaluating the sensitivity coefficients which measure the sensitivity of the buckling and postbuckling responses to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of variations in the laminate stacking sequence, fiber orientation, number of layers and aspect ratio of the panels on their thermomechanical buckling and postbuckling responses and their sensitivity coefficients.

Noor, Ahmed K.↗