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NASA NTRS1979

Does Venus wobble

The free wobble damping time for Venus due to solar tides and rotational flexing is found to be approximately 700,000 times Q sub omega years, where Q sub omega is the dissipation function associated with the wobble frequency. The slow spin and expected small (nonhydrostatic) J2 predict a very long wobble period of about 100,000 years. As a result, a simple scaling of the earth's Chandler wobble excitation rate to that of Venus suggests that an appreciable wobble could exist. Detection (or lack thereof) of a free wobble may thus place constraints on the dynamic activity (e.g., mantle convection, Venusquakes, etc.) of the Venus interior.

Yoder, C. F.↗

NASA NTRS1990

Galerkin approximations for dissipative magnetohydrodynamics

A Galerkin approximation scheme is proposed for voltage-driven, dissipative magnetohydrodynamics. The trial functions are exact eigenfunctions of the linearized continuum equations and represent helical deformations of the axisymmetric, zero-flow, driven steady state. The lowest nontrivial truncation is explored: one axisymmetric trial function and one helical trial function each for the magnetic and velocity fields. The system resembles the Lorenz approximation to Benard convection, but in the region of believed applicability, its dynamical behavior is rather different, including relaxation to a helically deformed state similar to those that have emerged in the much higher resolution computations of Dahlburg et al.

Chen, Hudong↗

NASA NTRS1995

An active magnetic bearing with high T(sub c) superconducting coils and ferromagnetic cores

A proof-of-feasibility demonstration showed that high-T(sub c) superconductor (HTS) coils can be used in a high-load, active magnetic bearing in LN2. A homopolar radial bearing with commercially wound HTS (Bi 2223) bias and control coils produced over 890 N (200 lb) radial load capacity (measured non-rotatings) and supported a shaft to 14,000 rpm. The goal was to show that HTS coils can operate stably with ferromagnetic cores in a feedback controlled system at a current density similar to that for Cu in LN2. The bias coil, wound with non-twisted, multifilament HTS conductor, dissipated negligible power for its direct current. The control coils, wound with monofilament HTS sheathed in Ag, dissipated negligible power for direct current. AC losses increased rapidly with frequency and quadratically with AC amplitude. Above about 2 Hz, the effective resistance of the control coils exceeds that of the silver which is in electrical parallel with the oxide superconductor. These results show that twisted multifilament conductor is not needed for stable levitation but may be desired to reduce control power for sizable dynamic loads.

Brown, G. V.↗

NASA NTRS2009

Liquid-Propellant Rocket Engine Throttling: A Comprehensive Review

Liquid-Propellant Rocket Engines (LREs) are capable of on-command variable thrust or thrust modulation, an operability advantage that has been studied intermittently since the late 1930s. Throttleable LREs can be used for planetary entry and descent, space rendezvous, orbital maneuvering including orientation and stabilization in space, and hovering and hazard avoidance during planetary landing. Other applications have included control of aircraft rocket engines, limiting of vehicle acceleration or velocity using retrograde rockets, and ballistic missile defense trajectory control. Throttleable LREs can also continuously follow the most economical thrust curve in a given situation, compared to discrete throttling changes over a few select operating points. The effects of variable thrust on the mechanics and dynamics of an LRE as well as difficulties and issues surrounding the throttling process are important aspects of throttling behavior. This review provides a detailed survey of LRE throttling centered around engines from the United States. Several LRE throttling methods are discussed, including high-pressure-drop systems, dual-injector manifolds, gas injection, multiple chambers, pulse modulation, throat throttling, movable injector components, and hydrodynamically dissipative injectors. Concerns and issues surrounding each method are examined, and the advantages and shortcomings compared.

Casiano, Matthew↗

NASA NTRS2011

Wireless Inductive Power Device Suppresses Blade Vibrations

Vibration in turbomachinery can cause blade failures and leads to the use of heavier, thicker blades that result in lower aerodynamic efficiency and increased noise. Metal and/or composite fatigue in the blades of jet engines has resulted in blade destruction and loss of lives. Techniques for suppressing low-frequency blade vibration, such as gtuned circuit resistive dissipation of vibratory energy, h or simply "passive damping," can require electronics incorporating coils of unwieldy dimensions and adding unwanted weight to the rotor. Other approaches, using vibration-dampening devices or damping material, could add undesirable weight to the blades or hub, making them less efficient. A wireless inductive power device (WIPD) was designed, fabricated, and developed for use in the NASA Glenn's "Dynamic Spin Rig" (DSR) facility. The DSR is used to simulate the functionality of turbomachinery. The relatively small and lightweight device [10 lb (approx.=4.5 kg)] replaces the existing venerable and bulky slip-ring. The goal is the eventual integration of this technology into actual turbomachinery such as jet engines or electric power generators, wherein the device will facilitate the suppression of potentially destructive vibrations in fan blades. This technology obviates slip rings, which require cooling and can prove unreliable or be problematic over time. The WIPD consists of two parts: a remote element, which is positioned on the rotor and provides up to 100 W of electrical power to thin, lightweight piezoelectric patches strategically placed on/in fan blades; and a stationary base unit that wirelessly communicates with the remote unit. The base unit supplies inductive power, and also acts as an input and output corridor for wireless measurement, and active control command to the remote unit. Efficient engine operation necessitates minimal disturbance to the gas flow across the turbine blades in any effort to moderate blade vibration. This innovation makes it possible to moderate vibration on or in turbomachinery blades by providing 100 W of wireless electrical power and actuation control to thin, lightweight vibration-suppressing piezoelectric patches (eight actuation and eight sensor patches in this prototype, for a total of 16 channels) positioned strategically on the surface of, or within, titanium fan blades, or embedded in composite fan blades. This approach moves significantly closer to the ultimate integration of "active" vibration suppression technology into jet engines and other turbomachinery devices such as turbine electrical generators used in the power industry. The novel feature of this device is in its utilization of wireless technology to simultaneously sense and actively control vibration in rotating or stationary turbomachinery blades using piezoelectric patches. In the past, wireless technology was used solely for sensing and diagnostics. This technology, however, will accomplish much more, in terms of simultaneously sensing, suppressing blade vibration, and making it possible for detailed study of vibration impact in turbomachinery blades.

Morrison, Carlos R.↗

NASA NTRS2011

Broken Ergodicity in MHD Turbulence in a Spherical Domain

Broken ergodicity (BE) occurs in Fourier method numerical simulations of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence. Although naive statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that low-wave-number coefficients have non-zero mean values that can be very large compared to the associated standard deviation. In other words, large-scale coherent structure (i.e., broken ergodicity) in homogeneous MHD turbulence can spontaneously grow out of random initial conditions. Eigenanalysis of the modal covariance matrices in the probability density functions of ideal statistical theory leads to a theoretical explanation of observed BE in homogeneous MHD turbulence. Since dissipation is minimal at the largest scales, BE is also relevant for resistive magnetofluids, as evidenced in numerical simulations. Here, we move beyond model magnetofluids confined by periodic boxes to examine BE in rotating magnetofluids in spherical domains using spherical harmonic expansions along with suitable boundary conditions. We present theoretical results for 3-D and 2-D spherical models and also present computational results from dynamical simulations of 2-D MHD turbulence on a rotating spherical surface. MHD turbulence on a 2-D sphere is affected by Coriolus forces, while MHD turbulence on a 2-D plane is not, so that 2-D spherical models are a useful (and simpler) intermediate stage on the path to understanding the much more complex 3-D spherical case.

Shebalin, John V.↗

NASA NTRS2020

Application of Quasi-Static Modal Analysis to an Orion Multi-Purpose Crew Vehicle Test

Bolted structural joints often exhibit load-dependent stiffness and energy dissipation that leads to nonlinear, amplitude dependent frequency and damping in the structure. As an alternative to direct integration of the nonlinear equations of motion, quasi-static modal analysis (QSMA) determines the dependence of frequency and damping on response amplitude using loading behavior from nonlinear static analyses. QSMA has previously been demonstrated to substantially reduce computational cost and maintain accuracy relative to full nonlinear dynamic simulation. This work explores the applicability of QSMA to a complex, large-scale aerospace structure. QSMA is employed to analyze a nonlinear model of test hardware developed to support the Orion Multi-Purpose Crew Vehicle program, which exhibited nonlinear behavior during dynamic testing at flight-like load levels. In addition to the extraction of amplitude-dependent frequency and damping curves, a Bouc-Wen hysteresis model was used in conjunction with the quasi-static results to develop nonlinear, uncoupled, time-domain modal equations of motion for the structure. Excellent agreement was observed between the reduced and full-order nonlinear models, encouraging future employment of QSMA to support accurate and efficient model reduction of structures with bolted joint nonlinearities.

QSMA↗

NASA NTRS1986

Magnetic energy storage and conversion in the solar atmosphere

According to the approach employed in this investigation, particularly important simple configurations of magnetic field and plasma are identified, and it is attempted to achieve an understanding of the large-scale dynamic processes and transformations which these systems can undergo. Fundamental concepts are discussed, taking into account aspects of magnetic energy generation, ideal MHD theory, non-MHD properties, the concept of 'anomalous' resistivity, and global electrodynamic coupling. Questions of magnetically controlled energy conversion are examined, giving attention to magnetic modifications of plasma transport, the transition region structure and flows, channeling and acceleration of plasma, channeling and dissipation of MHD waves, and anomalous dissipation of field-aligned currents. A description of the characteristics of magnetohydrodynamic energy conversion is also provided, and outstanding questions are discussed.

Spicer, D. S.↗

NASA NTRS1989

Numerical studies of identification in nonlinear distributed parameter systems

An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.

Banks, H. T.↗

NASA NTRS1997

The Implicit and Explicit alpha-mu Schemes

Artificial numerical dissipation is an important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional numerical schemes can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate numerical schemes such that artificial numerical dissipation will not overwhelm physical dissipation. Specifically, these schemes have the property that numerical dissipation vanishes when the physical viscosity goes to zero. These new schemes therefore accurately model the physical dissipation even when it is extremely small. The method of space-time conservation element and solution element, currently under development, is a nontraditional numerical method for solving conservation laws. The method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. Explicit solvers for model and fluid dynamic conservation laws have previously been investigated. In this paper, we introduce a new concept in the design of implicit schemes, and use it to construct two highly accurate solvers for a convection-diffusion equation. The two schemes become identical in the pure convection case, and in the pure diffusion case. The implicit schemes are applicable over the whole Reynolds number range, from purely diffusive equations to purely inviscid (convective) equations. The stability and consistency of the schemes are analyzed, and some numerical results are presented. It is shown that, in the inviscid case, the new schemes become explicit and their amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme. We also construct an explicit solver with the treatment of diffusion being based on that in the implicit solvers. The explicit solver has only a CFL stability limitation on the Courant number, yet it retains the second-order spatial accuracy of the implicit schemes.

Chang, Sin-Chung↗

NASA NTRS2014

Resonant Tidal Excitation of Internal Waves in the Earth's Fluid Core

It has long been speculated that there is a stably stratified layer below the core-mantle boundary, and two recent studies have improved the constraints on the parameters describing this stratification. Here we consider the dynamical implications of this layer using a simplified model. We first show that the stratification in this surface layer has sensitive control over the rate at which tidal energy is transferred to the core. We then show that when the stratification parameters from the recent studies are used in this model, a resonant configuration arrives whereby tidal forces perform elevated rates of work in exciting core flow. Specifically, the internal wave speed derived from the two independent studies (150 and 155 m/s) are in remarkable agreement with the speed (152 m/s) required for excitation of the primary normal mode of oscillation as calculated from full solutions of the Laplace Tidal Equations applied to a reduced-gravity idealized model representing the stratified layer. In evaluating this agreement it is noteworthy that the idealized model assumed may be regarded as the most reduced representation of the stratified dynamics of the layer, in that there are no non-essential dynamical terms in the governing equations assumed. While it is certainly possible that a more realistic treatment may require additional dynamical terms or coupling, it is also clear that this reduced representation includes no freedom for coercing the correlation described. This suggests that one must accept either (1) that tidal forces resonantly excite core flow and this is predicted by a simple model or (2) that either the independent estimates or the dynamical model does not accurately portray the core surface layer and there has simply been an unlikely coincidence between three estimates of a stratification parameter which would otherwise have a broad plausible range.

Geodynamo↗

NASA NTRS1985

Defect-phase-dynamics approach to statistical domain-growth problem of clock models

The growth of statistical domains in quenched Ising-like p-state clock models with p = 3 or more is investigated theoretically, reformulating the analysis of Ohta et al. (1982) in terms of a phase variable and studying the dynamics of defects introduced into the phase field when the phase variable becomes multivalued. The resulting defect/phase domain-growth equation is applied to the interpretation of Monte Carlo simulations in two dimensions (Kaski and Gunton, 1983; Grest and Srolovitz, 1984), and problems encountered in the analysis of related Potts models are discussed. In the two-dimensional case, the problem is essentially that of a purely dissipative Coulomb gas, with a sq rt t growth law complicated by vertex-pinning effects at small t.

Kawasaki, K.↗

NASA NTRS1988

Gravitational instability in two-phase disks and the origin of the moon

Two-phase disks may be gravitationally unstable at temperatures or surface densities at which a disk composed of either single phase would be highly stable. It is argued that two-phase disks can achieve a marginally unstable state (in addition to a highly unstable state that leads to fragmentation), limited by the ability of the photosphere to radiate the energy dissipated in the disk. A self-consistent prescription for the viscosity induced by the slow instabilities is provided. Two-phase disks are more centrally condensed than single-phase disks, and their secular cooling time may be comparable to their spreading time. A circumterrestrial disk of sufficient mass to form the moon provides a detailed example of all the preceding points. Its stability, structure, and dynamical evolution are investigated, and it is concluded that its spreading time is short (about 100 yr); the moon is formed molten, or partially molten; the moon's initial orbit lies in the earth's equatorial plane; and only a small fraction of the disk mass is lost in a wind, although this may represent a substantial fraction of volatiles. Most of these conclusions are independent of how the disk was formed, e.g., from a giant impact.

Thompson, Christopher↗

NASA NTRS2007

Coronal Heating, Weak MHD Turbulence, and Scaling Laws

Long-time high-resolution simulations of the dynamics of a coronal loop in Cartesian geometry are carried out, within the framework of reduced magnetohydrodynamics (RMHD), to understand coronal heating driven by the motion of field lines anchored in the photosphere. We unambiguously identify MHD anisotropic turbulence as the physical mechanism responsible for the transport of energy from the large scales, where energy is injected by photospheric motions, to the small scales, where it is dissipated. As the loop parameters vary, different regimes of turbulence develop: strong turbulence is found for weak axial magnetic fields and long loops, leading to Kolmogorov-like spectra in the perpendicular direction, while weaker and weaker regimes (steeper spectral slopes of total energy) are found for strong axial magnetic fields and short loops. As a consequence we predict that the scaling of the heating rate with axial magnetic field intensity B, which depends on the spectral index of total energy for given loop parameters, must vary from B3/2 for weak fields to B2 for strong fields at a given aspect ratio. The predicted heating rate is within the lower range of observed active region and quiet-Sun coronal energy losses.

corona↗

NASA NTRS1982

The dynamics of fibril magnetic fields. I - Effect of flux tubes on convection. II - The mean field equations

Observations have established the general fibril state of the magnetic field at the visible surface of the sun. This extraordinary state of the field, in separate intense flux tubes, implies that the convection has a relatively permanent, closed topology, in spite of the large Reynolds number. This paper explores some of the effects of the separate flux tubes on the convective motions, generally pushing the convective cells toward aligning their downdrafts with the flux tubes so as to minimize the dissipation.

Parker, E. N.↗

NASA NTRS1987

Two applications of potential vorticity thinking

The phenomena of dissipative destabilization of external Rossby waves and the acceleration of the zonal mean jet during baroclinic life cycles are described in terms of potential vorticity. The main principle of the potential temperature variations at rigid boundaries have the same effect on the interior flow as do sheets of potential vorticity located just within the boundaries. It is noted that the potential vorticity theory is useful for understanding the dynamical behavior of meterological phenomena.

Robinson, Walter A.↗

NASA NTRS1989

Computations of three-dimensional steady and unsteady viscous incompressible flows

The INS3D family of computational fluid dynamics computer codes is presented. These codes are used to as tools in developing and assessing algorithms for solving the incompressible Navier-Stokes equations for steady-state and unsteady flow problems. This work involves applying the codes to real-world problems involving complex three-dimensional geometries. The algorithms utilized include the method of pseudocompressibility including both central and upwind differencing, several types of artificial dissipation schemes, approximate factorization, and an implicit line-relaxation scheme. These codes have been validated using a wide range of problems including flow over a backward-facing step, driven cavity flow, flow through various types of ducts, and steady and unsteady flow over a circular cylinder. Many diverse flow applications have been solved using these codes including parts of the Space Shuttle Main Engine, problems in naval hydrodynamics, low-speed aerodynamics, and biomedical fluid flows. The presentation details several of these, including the flow through a Space Shuttle Main Engine inducer, vortex shedding behind a circular cylinder, and flow through an artificial heart.

Kwak, Dochan↗

NASA NTRS2007

A Time-Accurate Upwind Unstructured Finite Volume Method for Compressible Flow with Cure of Pathological Behaviors

A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods.

Loh, Ching Y.↗