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NASA NTRS1994

Analysis and prediction of ocean swell using instrumented buoys

During the period 20-23 September 1990, the remnants of Supertyphoon Flo moved into the central North Pacific Ocean with sustained wind speeds of 28 m/s. The strong wind and large fetch area associated with this storm generated long-period swell that propagated to the west coast of North America. National Data Buoy Center moored-buoy stations, located in a network that ranged from the Gulf of Alaska to the California Bight, provided wave spectral estimates of the swell from this storm. The greatest dominant wave periods measured were approximately 20-25 s, and significant wave heights measured ranged from 3 to 8 m. Wave spectra from an array of three nondirectional buoys are used to find the source of the long-period swell. Directional wave spectra from a heave-pitch-roll buoy are also used to make an independent estimate of the source of the swell. The ridge-line method, using time-frequency contour plots of wave spectral energy density, is used to determine the time of swell generation, which is used with the appropriate surface pressure analysis to infer the swell generation area. The diagnosed sources of the swell are also compared with nowcasts from the Global Spectral Ocean Wave Model of the Fleet Numerical Oceanography Center. A simple method of predicting the propagation of ocean swell, by applying a simple kinematic model of wave propagation to the estimated point and time source, is demonstrated.

Mettlach, Theodore↗

NASA NTRS1990

On the numerical solution of the dynamically loaded hydrodynamic lubrication of the point contact problem

The transient analysis of hydrodynamic lubrication of a point-contact is presented. A body-fitted coordinate system is introduced to transform the physical domain to a rectangular computational domain, enabling the use of the Newton-Raphson method for determining pressures and locating the cavitation boundary, where the Reynolds boundary condition is specified. In order to obtain the transient solution, an explicit Euler method is used to effect a time march. The transient dynamic load is a sinusoidal function of time with frequency, fractional loading, and mean load as parameters. Results include the variation of the minimum film thickness and phase-lag with time as functions of excitation frequency. The results are compared with the analytic solution to the transient step bearing problem with the same dynamic loading function. The similarities of the results suggest an approximate model of the point contact minimum film thickness solution.

Lim, Sang G.↗

NASA NTRS2005

A Concept for the Inclusion of Analytical and Computational Capability in Existing Systems for Measurement of Neutron Flux

For approximately two decades, efforts have been sponsored by NASA's Marshall Space Flight Center to make possible high-speed, automated classification and quantification of constituent materials in various harsh environments. MSFC, along with the Air Force/Arnold Engineering Development Center, has led the work, developing and implementing systems that employ principles of emission and absorption spectroscopy to monitor molecular and atomic particulates in gas plasma of rocket engine flow fields. One such system identifies species and quantifies mass loss rates in H2/O2 rocket plumes. Other gases have been examined and the physics of their detection under numerous conditions were made a part of the knowledge base for the MSFC/USAF team. Additionally, efforts are being advanced to hardware encode components of the data analysis tools in order to address real-time operational requirements for health monitoring and management. NASA has a significant investment in these systems, warranting a spiral approach that meshes current tools and experience with technological advancements. This paper addresses current systems - the Optical Plume Anomaly Detector (OPAD) and the Engine Diagnostic Filtering System (EDIFIS) - and discusses what is considered a natural progression: a concept for migrating them towards detection of high energy particles, including neutrons and gamma rays. The proposal outlines system development to date, basic concepts for future advancements, and recommendations for accomplishing them.

Patrick, Clinton↗

NASA NTRSDate not supplied

On A Stabilization of the Ingard-Myers Impedance Boundary Condition

It has been well-known that the Ingard-Myers impedance condition, while simple to apply, is subject to the hydrodynamic Kelvin-Helmholtz instability due to its use of a vortex sheet in modeling the flow at the liner boundary. Recently, in the development of a time domain boundary element method for acoustic scattering by treated surfaces, it was found that by neglecting a certain second-order spatial derivative term in the Ingard-Myers formulation, the hydrodynamic instability can be avoided. The present paper aims to provide further analysis of this modified condition, hereby referred to as Truncated Ingard-Myers Impedance Boundary Condition (TIMIBC). It will be shown, based on the dispersion relations of linear waves, that the instability intrinsic to the Ingard-Myers condition is eliminated in the proposed new formulation. Quantitative assessments on the accuracy of TIMIBC for scattering of acoustic waves by lined surfaces will be carried out, and its effectiveness will be demonstrated by numerical examples. Specifically, the accuracy is assessed by comparing solutions obtained by the Ingard-Myers condition with that by the proposed TIMIBC where theoretical reflection coefficients at a lined surface are derived for cases of plane and spherical incident waves. It is found that the TIMIBC provides a good approximation to the original Ingard-Myers condition for flows of low to mid subsonic Mach numbers. Time domain implementations of TIMIBC are also discussed and illustrated with a numerical example using a finite difference scheme. As many studies have shown the Ingard-Myers condition to be the correct limit of boundary layer thickness going to zero, the proposed TIMIBC can offer a practical solution for overcoming the intrinsic instability associated with the Ingard-Myers condition.

Time Domain BEM↗

NASA NTRSDate not supplied

On A Stabilization of the Ingard-Myers Impedance Boundary Condition

Time Domain BEM↗

NASA NTRS1999

Solving Upwind-Biased Discretizations: Defect-Correction Iterations

This paper considers defect-correction solvers for a second order upwind-biased discretization of the 2D convection equation. The following important features are reported: (1) The asymptotic convergence rate is about 0.5 per defect-correction iteration. (2) If the operators involved in defect-correction iterations have different approximation order, then the initial convergence rates may be very slow. The number of iterations required to get into the asymptotic convergence regime might grow on fine grids as a negative power of h. In the case of a second order target operator and a first order driver operator, this number of iterations is roughly proportional to h-1/3. (3) If both the operators have the second approximation order, the defect-correction solver demonstrates the asymptotic convergence rate after three iterations at most. The same three iterations are required to converge algebraic error below the truncation error level. A novel comprehensive half-space Fourier mode analysis (which, by the way, can take into account the influence of discretized outflow boundary conditions as well) for the defect-correction method is developed. This analysis explains many phenomena observed in solving non-elliptic equations and provides a close prediction of the actual solution behavior. It predicts the convergence rate for each iteration and the asymptotic convergence rate. As a result of this analysis, a new very efficient adaptive multigrid algorithm solving the discrete problem to within a given accuracy is proposed. Numerical simulations confirm the accuracy of the analysis and the efficiency of the proposed algorithm. The results of the numerical tests are reported.

Diskin, Boris↗

NASA NTRS1987

Liquid oxygen sloshing in Space Shuttle External Tank

This paper describes a numerical simulation of the hydrodynamics within the liquid oxygen tank of the Space Shuttle External Tank during liftoff. Before liftoff, the tank is filled with liquid oxygen (LOX) to approximately 97 percent with the other 3 percent containing gaseous oxygen (GOX) and helium. During liftoff, LOX is drained from the bottom of the tank, and GOX is pumped into the tank's ullage volume. There is a delay of several seconds before the GOX reaches the tank which causes the ullage pressure to decrease for several seconds after liftoff; this pressure 'slump' is a common phenomenon in rocket propulsion. When four slosh baffles were removed from the tank, the ullage gas pressure dropped more rapidly than in all previous flights. The purpose of this analysis was to determine whether the removal of the baffles could have caused the increased pressure 'slump' by changing the LOX surface dynamics. The results show that the LOX surface undergoes very high vertical accelerations (up to 5 g) and, therefore, splashing almost certainly occurs. The number of baffles does not affect the surface if the structural motion is assumed; but, the number of baffles may affect the structural motion of the tank.

Kannapel, M. D.↗

NASA NTRS1988

Modifying PASVART to solve singular nonlinear 2-point boundary problems

To study the buckling and post-buckling behavior of shells and various other structures, one must solve a nonlinear 2-point boundary problem. Since closed-form analytic solutions for such problems are virtually nonexistent, numerical approximations are inevitable. This makes the availability of accurate and reliable software indispensable. In a series of papers Lentini and Pereyra, expanding on the work of Keller, developed PASVART: an adaptive finite difference solver for nonlinear 2-point boundary problems. While the program does produce extremely accurate solutions with great efficiency, it is hindered by a major limitation. PASVART will only locate isolated solutions of the problem. In buckling problems, the solution set is not unique. It will contain singular or bifurcation points, where different branches of the solution set may intersect. Thus, PASVART is useless precisely when the problem becomes interesting. To resolve this deficiency we propose a modification of PASVART that will enable the user to perform a more complete bifurcation analysis. PASVART would be combined with the Thurston bifurcation solution: as adaptation of Newton's method that was motivated by the work of Koiter 3 are reinterpreted in terms of an iterative computational method by Thurston.

Fulton, James P.↗

NASA NTRS1989

Laboratory and theoretical studies of baroclinic processes

An understanding is being developed for processes which may be important in the atmosphere, and the definition and analysis of baroclinic experiments utilizing the geophysical fluid flow cells (GFFC) apparatus in microgravity space flights. Included are studies using numerical codes, theoretical models, and terrestrial laboratory experiments. The numerical modeling is performed in three stages: calculation of steady axisymmetric flow, calculation of fastest-growing linear eigenmodes, and nonlinear effects (first, wave-mean flow interactions, then wave-wave interactions). The code can accommodate cylindrical, spherical, or channel geometry. It uses finite differences in the vertical and meridional directions, and is spectral in the azimuthal. The theoretical work was mostly in the area of effects of topography upon the baroclinic instability problem. The laboratory experiments are performed in a cylindrical annulus which has a temperture gradient imposed upon the lower surface and an approximately isothermal outer wall, with the upper and inner surfaces being nominally thermally insulating.

Miller, Timothy↗

NASA NTRS1990

Singular perturbation analysis of AOTV-related trajectory optimization problems

The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.

Calise, Anthony J.↗

NASA NTRS1999

Hydrodynamic Stability and Magnetic Reconnection in Disks and Stars

The purpose of this grant is to study parametric instability. The simplest example of parametric instability is a harmonic oscillator with a periodic modulation of the spring constant. If the modulation frequency is close to twice the natural frequency of the oscillator, the amplitude of oscillation tends to grow exponentially. The growth rate is proportional to the strength of the modulation, but it also depends upon the closeness to resonance of the two frequencies, and upon natural damping rate or "Q" of the oscillator. Parametric instabilities are very common in physics. A familiar example is a jogger's ponytail--normally a very strongly damped pendulum, it can be destabilized by the variation in effective gravity during the jogger's stride. Observation confirms that the period of the pendulum is half that of the jogger's vertical motion. In astrophysics, parametric instability may occur by external tidal forcing, or by interaction among eigenmodes. In the latter case, an energetic eigenmode may destabilize modes of half its frequency, provided some weak nonlinearity exists to couple them. Under a previous Astrophysical Theory grant (NAGW-2419), the PI discovered a parametric instability of tidally forced disks such as the accretion disks in cataclysmic variables and X ray binaries [2]. The destabilized modes are tightly-wound, incompressible, three-dimensional waves analogous to g-modes and r-modes in stars. Later work has confirmed our analysis [4]. It was hoped that these modes might provide a source of turbulence and angular momentum transport in accretion disks. However, a follow-up investigation of this instability by local numerical simulations, although confirming the analytically estimated growth rates, found negligible angular momentum flux [3]. Other work, partly supported by the ATP, now strongly indicates that the transport mechanism in such disks is magnetohydrodynamic turbulence [6]. Nevertheless, the parametric mechanism may truncate the outer edges of disks in close binaries [2], and it may be important in disks of very low ionization such as protostellar disks, or even cataclysmic-variable disks in quiescence where the MHD mechanism may be ineffective [5]. All analyses up to 1996 were done in a local approximation where the orbital frequency, shear rate, and tidal field were treated as constants. The locally computed growth rate turns out to depend strongly on radius, and it was unclear how to average these local rates to obtain the correct global rate. This is a critical issue for accretion disks in close binaries, because the local growth rate is comparable to the orbital frequency towards the outer edge of the disk but decreases rapidly inwards. Paper #1 examined this issue in a simplified global model where the destabilizing terms vary with position. We found that the global growth rate is essentially equal to the maximum local rate, provided that the latter is smoothed over a radial range equal to the distance that the destabilized wave propagates at its group speed in one growth time. Thus, in an accretion disk, waves would grow rapidly in the outer parts but would propagate both inwards and outwards at a maximum group speed of order the disk thickness divided by the orbital period.

Goodman, Jeremy↗

NASA NTRS2010

Mud Volcanoes - Analogs to Martian Cones and Domes (by the Thousands!)

Mud volcanoes are mounds formed by low temperature slurries of gas, liquid, sediments and rock that erupt to the surface from depths of meters to kilometers. They are common on Earth, with estimates of thousands onshore and tens of thousands offshore. Mud volcanoes occur in basins with rapidly-deposited accumulations of fine-grained sediments. Such settings are ideal for concentration and preservation of organic materials, and mud volcanoes typically occur in sedimentary basins that are rich in organic biosignatures. Domes and cones, cited as possible mud volcanoes by previous authors, are common on the northern plains of Mars. Our analysis of selected regions in southern Acidalia Planitia has revealed over 18,000 such features, and we estimate that more than 40,000 occur across the area. These domes and cones strongly resemble terrestrial mud volcanoes in size, shape, morphology, associated flow structures and geologic setting. Geologic and mineralogic arguments rule out alternative formation mechanisms involving lava, ice and impacts. We are studying terrestrial mud volcanoes from onshore and submarine locations. The largest concentration of onshore features is in Azerbaijan, near the western edge of the Caspian Sea. These features are typically hundreds of meters to several kilometers in diameter, and tens to hundreds of meters in height. Satellite images show spatial densities of 20 to 40 eruptive centers per 1000 square km. Many of the features remain active, and fresh mud flows as long as several kilometers are common. A large field of submarine mud volcanoes is located in the Gulf of Cadiz, off the Atlantic coasts of Morocco and Spain. High-resolution sonar bathymetry reveals numerous km-scale mud volcanoes, hundreds of meters in height. Seismic profiles demonstrate that the mud erupts from depths of several hundred meters. These submarine mud volcanoes are the closest morphologic analogs yet found to the features in Acidalia Planitia. We are also conducting laboratory analyses of surface samples collected from mud volcanoes in Azerbaijan, Taiwan and Japan. X-ray diffraction, visible / near infrared reflectance spectroscopy and Raman spectroscopy show that the samples are dominated by mixed-layer smectite clays, along with quartz, calcite and pyrite. Thin section analysis by optical and scanning electron microscopy confirms the mineral identifications. These samples also contain chemical and morphological biosignatures, including common microfossils, with evidence of partial replacement by pyrite. The bulk samples contain approximately 1 wt% total organic carbon and 0.4 mg / gm volatile hydrocarbons. The thousands of features in Acidalia Planitia cited as analogous to terrestrial mud volcanoes clearly represent an important element in the sedimentary record of Mars. Their location, in the distal depocenter for massive Hesperian-age floods, suggests that they contain fine-grained sediments from a large catchment area in the martian highlands. We have proposed these features as a new class of exploration target that can provide access to minimally-altered material from significant depth. By analogy to terrestrial mud volcanoes, these features may also be excellent sites for the sampling martian organics and subsurface microbial life, if such exist or ever existed.

Allen, Carlton C.↗

NASA NTRS1993

Computational analysis of off-design waveriders

Comprehensive inviscid and viscous numerical simulations of hypersonic flow past nonconical rounded-nose waveriders are presented. The flow fields and aerodynamic forces at off-design conditions are determined inviscidly by a space-marching CFD code with the initial-data plane provided by a time-marching Navier-Stokes CFD code. Off-design conditions include off-design Mach numbers, angles of attack, and rounded leading edges. A wide range of waverider configurations is investigated and compared. These calculations show the effects of viscous interactions, which are influential near the leading edges, and determine the viscous drag. The inviscid calculations show that L/D decreases as freestream M increases (with alpha = 0). At the on-design Mach numbers, the maximum L/D may occur at slight positive or negative alpha, depending on the shape of the waverider, and zero lift occurs at a negative alpha approximately equal to half of the body thickness. The effects of slight leading-edge blunting produce only local effects in the flow field and small losses in L/D.

He, X.↗

NASA NTRS1990

Numerical simulation of rarefied gas flow through a slit

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

Keith, Theo G., Jr.↗

NASA NTRS1973

Comparison of finite-difference schemes for analysis of shells of revolution

Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.

Noor, A. K.↗

NASA NTRS1987

The structure of the time-dependent interstellar shocks and grain destruction in the interstellar medium

A new theoretical analysis of the structure of interstellar shocks and the grain dynamics of these shocks is presented. The basic hydrodynamic equations for J-shocks in interstellar gas are given in which shock-driving pressure is allowed to be weakly time-dependent and the grains are treated as a separate two-dimensional fluid. Specific equations for the grain dynamics in the cooling postshock gas are derived. An analytic theory for the propagation of a shock driven into an interstellar cloud by the blast wave of a supernova remnant which sweeps over the cloud is developed. An improved calculation of the grain charge in postshock gas is described, giving a simple analytic approximation for the results. The consequences of including these processes in the numerical code of Seab and Shull (1983) are addressed, including the effect of realistic magnetic fields in low-density gas.

Mckee, Christopher F.↗

NASA NTRS2006

Modeling Gravitational Radiation Waveforms from Black Hole Mergers

Gravitational radiation from merging binary black hole systems is anticipated as a key source for gravitational wave observations. Ground-based instruments, such as the Laser Interferometer Gravitational-wave Observatory (LIGO) may observe mergers of stellar-scale black holes, while the space-based Laser Interferometer Space Antenna (LISA) observatory will be sensitive to mergers of massive galactic-center black holes over a broad range of mass scales. These cataclysmic events may emit an enormous amount of energy in a brief time. Gravitational waves from comparable mass mergers carry away a few percent of the system's mass-energy in just a few wave cycles, with peak gravitational wave luminosities on the order of 10^23 L_Sun. Optimal analysis and interpretation of merger observation data will depend on developing a detailed understanding, based on general relativistic modeling, of the radiation waveforms. We discuss recent progress in modeling radiation from equal mass mergers using numerical simulations of Einstein's gravitational field equations, known as numerical relativity. Our simulations utilize Adaptive Mesh Refinement (AMR) to allow high-resolution near the black holes while simultaneously keeping the outer boundary of the computational domain far from the black holes, and making it possible to read out gravitational radiation waveforms in the weak-field wave zone. We discuss the results from simulations beginning with the black holes orbiting near the system's innermost stable orbit, comparing the recent simulations with earlier "Lazarus" waveform estimates based on an approximate hybrid numerical/perturbative technique.

Baker, J. G.↗

NASA NTRS2015

Fuel Distribution Estimate via Spin Period to Precession Period Ratio for the Advanced Composition Explorer

The spin period to precession period ratio of a non-axisymmetric spin-stabilized spacecraft, the Advanced Composition Explorer (ACE), was used to estimate the remaining mass and distribution of fuel within its propulsion system. This analysis was undertaken once telemetry suggested that two of the four fuel tanks had no propellant remaining, contrary to pre-launch expectations of the propulsion system performance. Numerical integration of possible fuel distributions was used to calculate moments of inertia for the spinning spacecraft. A Fast Fourier Transform (FFT) of output from a dynamics simulation was employed to relate calculated moments of inertia to spin and precession periods. The resulting modeled ratios were compared to the actual spin period to precession period ratio derived from the effect of post-maneuver nutation angle on sun sensor measurements. A Monte Carlo search was performed to tune free parameters using the observed spin period to precession period ratio over the life of the mission. This novel analysis of spin and precession periods indicates that at the time of launch, propellant was distributed unevenly between the two pairs of fuel tanks, with one pair having approximately 20% more propellant than the other pair. Furthermore, it indicates the pair of the tanks with less fuel expelled all of its propellant by 2014 and that approximately 46 kg of propellant remains in the other two tanks, an amount that closely matches the operational fuel accounting estimate. Keywords: Fuel Distribution, Moments of Inertia, Precession, Spin, Nutation

Moment of Inertia↗