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NASA NTRS1990

Obliquity histories of Earth and Mars: Influence of inertial and dissipative core-mantle coupling

For both the Earth and Mars, secular variations in the angular separation of the spin axis from the orbit normal are suspected of driving major climatic changes. There is considerable interest in determining the amplitude and timing of these obliquity variations. If the orientation of the orbital plane were inertially fixed, and the planet were to act as a rigid body in it response to precessional torques, the spin axis would simply precess around the orbit at a fixed obliquity and at a uniform angular rate. The precession rate parameter depends on the principal moments of inertia and rotation rate of the perturbed body, and on the gravitational masses and semiminor axes of the perturbing bodies. For Mars, the precession rate is not well known, but probably lies in the interval 8 to 10 arcsec/year. Gravitational interactions between the planets lead to secular motions of the orbit planes. In the rigid body case, the spin axis still attempts to precess about the instantaneous orbit normal, but now the obliquity varies. The hydrostatic figure of a planet represents a compromise between gravitation, which attempts to attain spherical symmetry, and rotation, which prefers cylindrical symmetry. Due to their higher mean densities the cores of the Earth and Mars will be more nearly spherical than the outer layers of these planets. On short time scales it is appropriate to consider the core to be an inviscid fluid constrained to move with the ellipsoidal region bounded by the rigid mantle. The inertial coupling provided by this mechanism is effective whenever the ellipticicy of the container exceeds the ratio of precessional to rotational rates. If the mantle were actually rigid, this would be an extremely effective type of coupling. However, on sufficiently long time scales, the mantle will deform viscously and can accommodate the motions of the core fluid. A fundamentally different type of coupling is provided by electromagnetic or viscous torques. This type of coupling is likely to be most important on longer time scales. In each case, the mantle exerts an equal and opposite torque on the core.

Bills, Bruce G.↗

NASA NTRS1990

Analytical and experimental investigations of the oblique detonation wave engine concept

Wave combustors, which include the oblique detonation wave engine (ODWE), are attractive propulsion concepts for hypersonic flight. These engines utilize oblique shock or detonation waves to rapidly mix, ignite, and combust the air-fuel mixture in thin zones in the combustion chamber. Benefits of these combustion systems include shorter and lighter engines which require less cooling and can provide thrust at higher Mach numbers than conventional scramjets. The wave combustor's ability to operate at lower combustor inlet pressures may allow the vehicle to operate at lower dynamic pressures which could lessen the heating loads on the airframe. The research program at NASA-Ames includes analytical studies of the ODWE combustor using Computational Fluid Dynamics (CFD) codes which fully couple finite rate chemistry with fluid dynamics. In addition, experimental proof-of-concept studies are being performed in an arc heated hypersonic wind tunnel. Several fuel injection design were studied analytically and experimentally. In-stream strut fuel injectors were chosen to provide good mixing with minimal stagnation pressure losses. Measurements of flow field properties behind the oblique wave are compared to analytical predictions.

Menees, Gene P.↗

NASA NTRS1990

Static aeroelastic analysis of a three-dimensional oblique wing

A capability to perform static aeroelastic analyses of an oblique wing at arbitrary skew positions was developed based on the framework of the MSC/NASTRAN static aeroelastic analysis. By means of DMAP alterations, a portion of the subsonic static aeroelastic analysis scheme was modified to insert an aerodynamic influence coefficient matrix created externally by the NASA-Ames aerodynamic panel codes. The modified scheme can cover the subsonic as well as the supersonic range for both symmetric and asymmetric configurations. Static aeroelastic responses of the oblique wing are studied at two skew angles and, in particular, the capability to calculate 3D camber effects on the aerodynamic properties of the wing is investigated. Various aerodynamic coefficients of the rigid oblique wing are computed for two Mach numbers, 0.7 and 1.4, and the angle of attack is varied from -5 through 15 deg. Also, the wing flexibility effects on the aerodynamic coefficients and the displacement are examined at a Mach number of 0.7 for a 45-deg swept wing.

Lee, I.↗

NASA NTRS1992

Frequency variations of the earth's obliquity and the 100-kyr ice-age cycles

Changes in the earth's climate are induced by variations in the earth's orbital parameters which modulate the seasonal distribution of solar radiation. Periodicities in the geological climate record with cycles of 100, 41, and 23 kyr have been linked with changes in obliquity, eccentricity, and precession of the equinoxes. The effect of variations of eccentricity during a 100 kyr period is weak relative to the signals from obliquity and precession variations and it may therefore be expected that the 100 kyr signal in the climate record would be of low intensity. However, this signal dominates the climate record and internal nonlinear processes within the climate system have previously been proposed to account for this fact. The author shows that variations in the frequency of the obliquity cycle can give rise to strong 100-kyr forcing of climate.

Liu, Han-Shou↗

NASA NTRS1991

Analytical and experimental investigations of the oblique detonation wave engine concept

Wave combustors, which include the Oblique Detonation Wave Engine (ODWE), are attractive propulsion concepts for hypersonic flight. These engines utilize oblique shock or detonation waves to rapidly mix, ignite, and combust the air-fuel mixture in thin zones in the combustion chamber. Benefits of these combustion systems include shorter and lighter engines which will require less cooling and can provide thrust at higher Mach numbers than conventional scramjets. The wave combustor's ability to operate at lower combustor inlet pressures may allow the vehicle to operate at lower dynamic pressures which could lessen the heating loads on the airframe. The research program at NASA-Ames includes analytical studies of the ODWE combustor using CFD codes which fully couple finite rate chemistry with fluid dynamics. In addition, experimental proof-of-concept studies are being carried out in an arc heated hypersonic wind tunnel. Several fuel injection designs were studied analytically and experimentally. In-stream strut fuel injectors were chosen to provide good mixing with minimal stagnation pressure losses. Measurements of flow field properties behind the oblique wave are compared to analytical predictions.

Menees, Gene P.↗

NASA NTRS1993

The injection and acceleration of particles in oblique shocks - A unified Monte Carlo description

Important problems are discussed concerning the effects of shock geometry on the injection of thermal particles and the process of standard Fermi particle acceleration in general. In pursuit of a self-consistent model that simultaneously describes shock structure and particle acceleration in shocks of arbitrary obliquity, a Monte Carlo simulation developed for parallel shocks is generalized to address oblique geometries. Attention is given to initial results concerning the ways in which injection and acceleration efficiency varies with obliquity and Mach number.

Baring, Matthew G.↗

NASA NTRS1991

Jet ejecta mass upon oblique impact

Theoretical models in the jetting regime for symmetric and asymmetric impact of thin plates predict the mass and velocity of jetted material upon oblique impact. However, experimental constraints on the amount of material which form jets upon oblique impact are not known. A series of preliminary experiments were conducted in which tungsten (W) flyer plates at speeds of 1.5 to 2.0 km/s were obliquely impacted into carbon targets at 30 deg in the regime of jetting, yielding radiation temperatures in the about 3200 K range. Both framing-camera and flash X-ray imaging were conducted. Broad cm-sized craters induced by jet ejecta on 2024 Al witness plates were used to infer jet mass. We infer, from measured witness plate crater volumes, that jet masses in the range of 0.01 to 0.06 g are produced by a 32 mm diameter, 6 mm thick W impactor. This is about one to two orders of magnitude less than those calculated from present theoretical models. In contrast, in refractory material experiments, the mass of gabbro ejecta trapped in styrofoam is 0.52 g, which is similar to that calculated.

Yang, W.↗

NASA NTRS1993

The connection between Venus' free obliquity and its CMB oblateness

The most striking feature of Venus rotational state is its slow retrograde rotation which is apparently maintained by a balance between solid tidal friction and thermal tidal torques. Solid tides tend to drive the spin toward synchronous rotation while thermal tides drive it away. A balance is achieved at a specific rate because of the inverse frequency dependence of the thermal tide to the semi-diurnal heating. Atmospheric models have been constructed to estimate the thermal tidal torque based on ground heating. The solid friction dissipation factor Q approximately equal to 50 can be deduced assuming rotation has achieved steady state. The most perplexing feature of Venus orientation is its non-zero free obliquity epsilon approximately equal to 1.5 deg relative to its orbit. Although solid tides and perhaps atmospheric tides tend to increase the free obliquity on a time 1/K(sub t) approximately equal to 1 x 10(exp 8) yr, viscous friction (CMF) at a core-mantle boundary (CMB) resulting from the differential angular orientation Delta-epsilon of the core and mantle spin axes should have damped the free obliquity on a time scale as short as 10(exp 6) yr. One means of achieving a balance similar to that controlling rotation is to introduce a comparatively large CMB ellipticity e(sub c) to reduce Delta-epsilon such that there is a balance between solid-thermal tides and CMF. The balance depends not so much on the potential frequency dependence on the tides as on the quadratic dependence of CMF on Delta-epsilon if the layer is turbulent.

Yoder, C. F.↗

NASA NTRS1995

Time-dependent simulation of oblique MHD cosmic-ray shocks using the two-fluid model

Using a new, second-order accurate numerical method we present dynamical simulations of oblique MHD cosmic-ray (CR)-modified plane shock evolution. Most of the calculations are done with a two-fluid model for diffusive shock acceleration, but we provide also comparisons between a typical shock computed that way against calculations carried out using the more complete, momentum-dependent, diffusion-advection equation. We also illustrate a test showing that these simulations evolve to dynamical equilibria consistent with previously published steady state analytic calculations for such shocks. In order to improve understanding of the dynamical role of magnetic fields in shocks modified by CR pressure we have explored for time asymptotic states the parameter space of upstream fast mode Mach number, M(sub f), and plasma beta. We compile the results into maps of dynamical steady state CR acceleration efficiency, epsilon(sub c). We have run simulations using constant, and nonisotropic, obliquity (and hence spatially) dependent forms of the diffusion coefficient kappa. Comparison of the results shows that while the final steady states achieved are the same in each case, the history of CR-MHD shocks can be strongly modified by variations in kappa and, therefore, in the acceleration timescale. Also, the coupling of CR and MHD in low beta, oblique shocks substantially influences the transient density spike that forms in strongly CR-modified shocks. We find that inside the density spike a MHD slow mode wave can be generated that eventually steepens into a shock. A strong layer develops within the density spike, driven by MHD stresses. We conjecture that currents in the shear layer could, in nonplanar flows, results in enhanced particle accretion through drift acceleration.

Frank, Adam↗

NASA NTRS1995

Chaotic obliquity and the nature of the Martian climate

Recent calculations of the Martian obliquity suggests that it varies chaotically on timescales longer than about 10(exp 7) years and varies between about 0 and 60 deg. We examine the seasonal water behavior at obliquities between 40 and 60 deg. Up to several tens of centimeters of water may sublime from the polar caps each year, and possibly move to the equator, where it is more stable. The CO2 frost and CO2-H2O clathrate hydrate are stable in thepolar deposits below a few tens of meters depth, so that the polar cap could contain a significant CO2 reservoir. If CO2 is present, it could be left over from the early history of Mars; also, it could be released into the atmosphere during periods of high obliquity, causing occasional periods of more-clement climate.

Jakosky, Bruce M.↗

NASA NTRS1995

Particle interactions with obliquely propagating magnetosonic waves

Four cases of nonlinear obliquely propagating magnetosonic (MS) waves are considered using a test particle approach for particles interaction with (1) monochromatic waves propagating both sunward and antisunward, (2) monochromatic waves propagating unidirectionally toward the Sun, (3) a broad band spectrum, propagating both sunward and antisunward, and (4) a broadband spectrum, propagating sunward only. As the solar wind decelerates rapidly inside the bow shock, the interplanetary magnetic field (IMF) increases. Calculations have been performed taking into account such a spatially dependent IMF (based on observations). We find that significant particle acceleration is achieved for both the monochromatic wave and the 'turbulent' MS waves, for oblique propagation (angles between the interplanetary magnetic field and the propagation vector larger than 30 deg). This is due to the fact that at oblique angles resonance width increases. We have compared the relative acceleration of particles for the four cases. Pitch angle scattering and acceleration of particles are found to be much larger in the case of sunward and antisunward propagating waves than those for the sunward waves only. This is due to larger relative phase velocities in the two cases. Also, acceleration of particles is less in the case of a uniform magnetic field than that in the case of spatially increasing magnetic field. The particles get more pitch angle scattered and accelerated in the latter case.

Srivastava, Krishna M.↗

NASA NTRS1995

Material processing of convection-driven flow field and temperature distribution under oblique gravity

A set of mathematical formulation is adopted to study vapor deposition from source materials driven by heat transfer process under normal and oblique directions of gravitational acceleration with extremely low pressure environment of 10(exp -2) mm Hg. A series of time animation of the initiation and development of flow and temperature profiles during the course of vapor deposition has been obtained through the numerical computation. Computations show that the process of vapor deposition has been accomplished by the transfer of vapor through a fairly complicated flow pattern of recirculation under normal direction gravitational acceleration. It is obvious that there is no way to produce a homogeneous thin crystalline films with fine grains under such a complicated flow pattern of recirculation with a non-uniform temperature distribution under normal direction gravitational acceleration. There is no vapor deposition due to a stably stratified medium without convection for reverse normal direction gravitational acceleration. Vapor deposition under oblique direction gravitational acceleration introduces a reduced gravitational acceleration in vertical direction which is favorable to produce a homogeneous thin crystalline films. However, oblique direction gravitational acceleration also induces an unfavorable gravitational acceleration along horizontal direction which is responsible to initiate a complicated flow pattern of recirculation. In other words, it is necessary to carry out vapor deposition under a reduced gravity in the future space shuttle experiments with extremely low pressure environment to process vapor deposition with a homogeneous crystalline films with fine grains. Fluid mechanics simulation can be used as a tool to suggest most optimistic way of experiment with best setup to achieve the goal of processing best nonlinear optical materials.

Hung, R. J.↗

NASA NTRS1996

Computation of Thermally Perfect Properties of Oblique Shock Waves

A set of compressible flow relations describing flow properties across oblique shock waves, derived for a thermally perfect, calorically imperfect gas, is applied within the existing thermally perfect gas (TPG) computer code. The relations are based upon a value of cp expressed as a polynomial function of temperature. The updated code produces tables of compressible flow properties of oblique shock waves, as well as the original properties of normal shock waves and basic isentropic flow, in a format similar to the tables for normal shock waves found in NACA Rep. 1135. The code results are validated in both the calorically perfect and the calorically imperfect, thermally perfect temperature regimes through comparisons with the theoretical methods of NACA Rep. 1135, and with a state-of-the-art computational fluid dynamics code. The advantages of the TPG code for oblique shock wave calculations, as well as for the properties of isentropic flow and normal shock waves, are its ease of use, and its applicability to any type of gas (monatomic, diatomic, triatomic, polyatomic, or any specified mixture thereof).

Tatum, Kenneth E.↗

NASA NTRS2000

Acoustic Receptivity of a Blasius Boundary Layer with 2-D and Oblique Surface Waviness

An experimental investigation was conducted to examine acoustic receptivity and subsequent boundary-layer instability evolution for a Blasius boundary layer formed on a flat plate in the presence of two-dimensional (2-D) and oblique (3-D) surface waviness. The effect of the non-localized surface roughness geometry and acoustic wave amplitude on the receptivity process was explored. The surface roughness had a well defined wavenumber spectrum with fundamental wavenumber k (sub w). A planar downstream traveling acoustic wave was created to temporally excite the flow near the resonance frequency of an unstable eigenmode corresponding to k (sub ts) = k (sub w). The range of acoustic forcing levels, epsilon, and roughness heights, DELTA h, examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the forcing combination epsilon dot DELTA h resulted in subsequent nonlinear development of the Tollmien-Schlichting (T-S) wave. This study provided the first experimental evidence of a marked increase in the receptivity coefficient with increasing obliqueness of the surface waviness in excellent agreement with theory. Detuning of the 2-D and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber a,, and measuring the T-S response. For the configuration where laminar-to-turbulent breakdown occurred, the breakdown process was found to be dominated by energy at the fundamental and harmonic frequencies, indicative of K-type breakdown.

King, Rudolph A.↗

NASA NTRS2000

Giant Impacts and the Distribution of Planetary Obliquities

We have conducted a set of approximately 200 numerical experiments to test the hypothesis that a giant impact leading to the formation of Earth's Moon could have occurred tens of millions of years after most of the small debris in the inner Solar System had been incorporated into terrestrial planets or been removed from the region. More than half of these simulations ended with a giant impact between two of the five terrestrial planets that were initially present. Neglecting any rotational angular momentum prior to the collision, the merged planet typically has a rotation period of less than five hours. The mean planetary obliquity is 91.7 degrees, and the median is 87.9 degrees; thus, there is no statistically significant difference between the number of bodies with prograde rotation and the number with retrograde rotation. There is a paucity of planets with obliquity close to 90 degrees, but the total number of impacts was too small for this result to be of much significance. Several encounters leading to collisions are dominated by three-body effects, with the velocity at impact being slightly less than the free-space escape velocity of the two bodies; the obliquity distribution produced by these impacts appears to be random.

Lissauer, Jack J.↗

NASA NTRS2003

The Evolution of Oblique Impact Flow Fields Using Maxwell's Z Model

Oblique impacts are the norm rather than the exception for impact craters on planetary surfaces. This work focuses on the excavation of experimental oblique impact craters using the NASA Ames Vertical Gun Range (AVGR). Three-dimensional particle image velocimetry (3D PIV) is used to obtain quantitative data on ejection positions, three dimensional velocities and angles. These data are then used to constrain Maxwell's Z Model and follow the subsurface evolution of the excavation-stage flow-field center during oblique impacts.

Anderson, J. L. B.↗

NASA NTRS2003

The Evolution of Oblique Impact Flow Fields Using Maxwell's Z Model

Oblique impacts are the norm rather than the exception for impact craters on planetary surfaces. This work focuses on the excavation of experimental oblique impact craters using the NASA Ames Vertical Gun Range (AVGR). Three-dimensional particle image velocimetry (3D PIV) is used to obtain quantitative data on ejection positions, three-dimensional velocities and angles. These data are then used to test the applicability and limitations of Maxwell's Z Model in representing the subsurface evolution of the excavation-stage flow-field center during vertical and oblique impacts.

Anderson, J. L. B.↗

NASA NTRS2003

Magnetohydrodynamic Jump Conditions for Oblique Relativistic Shocks with Gyrotropic Pressure

Shock jump conditions, i.e., the specification of the downstream parameters of the gas in terms of the upstream parameters, are obtained for steady-state, plane shocks with oblique magnetic fields and arbitrary flow speeds. This is done by combining the continuity of particle number flux and the electromagnetic boundary conditions at the shock with the magnetohydrodynamic conservation laws derived from the stress-energy tensor. For ultrarelativistic and nonrelativistic shocks, the jump conditions may be solved analytically. For mildly relativistic shocks, analytic solutions are obtained for isotropic pressure using an approximation for the adiabatic index that is valid in high sonic Mach number cases. Examples assuming isotropic pressure illustrate how the shock compression ratio depends on the shock speed and obliquity. In the more general case of gyrotropic pressure, the jump conditions cannot be solved analytically with- out additional assumptions, and the effects of gyrotropic pressure are investigated by parameterizing the distribution of pressure parallel and perpendicular to the magnetic field. Our numerical solutions reveal that relatively small departures from isotropy (e.g., approximately 20%) produce significant changes in the shock compression ratio, r , at all shock Lorentz factors, including ultrarelativistic ones, where an analytic solution with gyrotropic pressure is obtained. In particular, either dynamically important fields or significant pressure anisotropies can incur marked departures from the canonical gas dynamic value of r = 3 for a shocked ultrarelativistic flow and this may impact models of particle acceleration in gamma-ray bursts and other environments where relativistic shocks are inferred. The jump conditions presented apply directly to test-particle acceleration, and will facilitate future self-consistent numerical modeling of particle acceleration at oblique, relativistic shocks; such models include the modification of the fluid velocity profile due to the contribution of energetic particles to the momentum and energy fluxes.

Double, Glen P.↗