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At least 505 records · Page 28

The evolution of rotating stars. 1: Method and exploratory calculations for a 7 solar mass star

A method was developed which allows us to study the evolution of rotating stars beyond the main sequence stage. Four different cases of redistribution of angular momentum in an evolving star are considered. Evolutionary sequences for a 7 solar mass star, rotating according to these different cases, were computed from the ZAMS to the double shell source stage. Each sequence was begun with a (typical) equatorial velocity of 210 km/sec. On the main sequence, the effects of rotation are of minor importance. As the core contracts during later stages, important effects arise in all physically plausible cases. The outer regions of the cores approach critical velocities and develop unstable angular velocity distributions. The effects of these instabilities should significantly alter the subsequent evolution.

Endal, A. S.↗

Momentum-Based Dynamics for Spacecraft with Chained Revolute Appendages

An efficient formulation is presented for a sub-class of multi-body dynamics problems that involve a six degree-of-freedom base body and a chain of N rigid linkages connected in series by single degree-of-freedom revolute joints. This general method is particularly well suited for simulations of spacecraft dynamics and control that include the modeling of an orbiting platform with or without internal degrees of freedom such as reaction wheels, dampers, and/or booms. In the present work, particular emphasis is placed on dynamic simulation of multi-linkage robotic manipulators. The differential equations of motion are explicitly given in terms of linear and angular momentum states, which can be evaluated recursively along a serial chain of linkages for an efficient real-time solution on par with the best of the O(N3) methods.

Queen, Steven↗

Adjusting a Full Body Model to Mitigate Inverse Kinematics Artifacts in Opensim

BACKGROUND: In support of Vibration Isolation and Stabilization (VIS) system development for Human Health Countermeasures (HHC) exercise systems in space, such as the European Enhanced Exploration Exercise Device (E4D) [1], dynamic quantities required to model the response of a proposed VIS while considering the effect of VIS motion on the forces between the human and VIS platform were obtained using motion capture data [2]. On occasion, large-amplitude oscillatory spikes were found in the subject’s linear and angular momentum derivatives, affecting analyses that depend on forces and moments derived from motion capture. The purpose of this investigation was to identify causes of these artifacts and techniques for their resolution. METHODS AND RESULTS: To obtain the required human dynamic quantities to drive the VIS simulation, motion capture data was collected containing recorded trajectories of passive retroreflective markers on body landmarks of an exercising subject. Since the full body Rajagopal model [3] was originally used to enhance gait analysis, upper body joints did not require large Ranges of Motion (ROM). We thus modified the Rajagopal model [4, 5] to allow it to be used for upper body intensive exercises like those common to the E4D. OpenSim Inverse Kinematics (IK) [6] was performed using these scaled subject models to generate the joint angles throughout the exercise while minimizing marker error. At times, the arms were observed to ‘snap’ from one configuration to another, causing spike artifacts. Following IK, a custom OpenSim plugin [7] was used to determine the required dynamic quantities including the rates of change of the linear and angular momenta of the human. Since motion capture is recorded at a larger time step than required by the VIS simulation, the human center of mass location was fit with splines and a second derivative taken to obtain the momentum derivative, allowing the VIS simulation to maintain conservation of momentum when appropriate. In a few cases during this stage, artifacts much larger than the expected noise of the second derivatives were introduced. Investigation of cases containing artifacts revealed several modifications that could be made to the OpenSim model to improve IK results. Since OpenSim models use Euler angles and rotation sequences, ‘gimbal lock’ would be encountered in the arms when raised 90 degrees to the side (e.g., T-pose, some hang clean exercise, etc.). This was resolved by reorienting the horizontal axes at the shoulder joint by 45 degrees, placing ‘gimbal lock’ outside common arm ROM, with the arm ROMs adjusted following this change. Elbow and wrist ROMs could also be adjusted to allow realistic motion while at the same time limiting the likelihood of unrealistic orientations. On occasion, the arms flipped backwards when raised above the head. This was prevented by using medial elbow markers in scaling and IK. When medial markers were not available, the acromial joint location in the unscaled model was shifted before model scaling to better align the arm with available markers. Lastly, artifacts which became apparent after taking the second derivatives of spline-fit data were found to occur in cases when the pelvis rotation limit prevented the full range of motion of an exercise. These issues were resolved by unclamping the pelvis rotation limit. Through this investigation, an understanding of conditions leading to IK artifacts was acquired allowing the automation of artifact detection. These artifact detection and mitigation techniques can be applied toward modeling of upper body motions in aerospace and other fields for improved IK results.

C A Bell↗

Global Geophysical Fluids Center of IERS

The Global Geophysical Fluids Center (GGFC) and its seven Special Bureaus (SB, for Atmosphere, Oceans, Tides, Hydrology, Mantle, Core and Gravity/Geocenter) were establishes by the International Earth Rotation Service in 1998, to support global geodynamic research. Mass transports in the geophysical fluids of the Earth system will cause observable geodynamic effects on a broad time scale.These include (1) variations in the solid Earth's rotation (in length-of-day and polar motion/nutation) via the conservation of angular momentum and effected by torques at the fluid-solid Earth interface; (2) changes in the global gravitational field according to Newton's gravitational law; and (3) motion in the center of mass of the solid Earth relative to that of the whole Earth ("geocenter") via the conservation of linear momentum. These minute signals have become observable by space geodetic techniques, primarily VLBI, SLR, GPS, and DORIS, and new exciting data will be available by space gravity, altimetry, SAR, and magnetic missions. In this sense the precise space geodetic techniques have become effective means of remote sensing of global mass transports. The GGFC and its SBs have the responsibility of supporting, facilitating, and providing services to the worldwide research community in the related research areas. We compute, analyze, compare, archive, and disseminate the time series of the angular momenta and the related torques, gravitational coefficients, and geocenter shift for all geophysical fluids, based on global observational data, and/or products from state-of-the-art models some of which assimilate such data. The computed quantities, algorithm and data formats are standardized. This paper reviews our activities, reports the status, and looks forward into the future.

Chao, Benjamin F.↗

The evolution of rotating stars. I - Method and exploratory calculations for a 7-solar-mass star

A method is developed which allows the evolution of rotating stars to be studied well beyond the main-sequence stage. Four different cases of redistribution of angular momentum in an evolving star are considered. Evolutionary sequences for a 7-solar-mass star, rotating according to these different cases, were computed from the zero-age main-sequence to the double-shell-source stage. Each sequence was begun with a (typical) equatorial rotational velocity of 210 km/s. On the main sequence, the effects of rotation are of minor importance. However, as the core contracts during later stages, important effects arise in all physically plausible cases. The outer regions of the cores approach critical velocities and develop unstable angular-velocity distributions. The effects of these instabilities should significantly alter the subsequent evolution.

Endal, A. S.↗

Development of a two-dimensional zonally averaged statistical-dynamical model. II - The role of eddy momentum fluxes in the general circulation and their parameterization

The role of eddy momentum fluxes in the general circulation was investigated using a two-dimensional zonally averaged statistical-dynamical model described by Yao and Stone (1987), which is almost two orders of magnitude faster than the three-dimensional climate model of Hansen et al. (1983). Results show that the vertical structure of the meridional eddy flux has relatively little impact on the general circulation, presumably because the vertical structure is strongly constrained by the thermal wind relation and surface friction. On the other hand, it was found that, in order to simulate accurately the general circulation and its response to climate changes, parameterization of the vertically integrated meridional eddy flux of angular momentum is necessary. A new parameterization of this eddy momentum transport was carried out, which is intended to represent the transport due to large-scale transient eddies arising from baroclinic instability.

Stone, Peter H.↗

Fall-Back Disks in Long and Short GRBS

We present numerical time-dependent calculations for fall-back disks relevant for GRBs in which the disk of material surrounding the black hole (BH) powering the GRB jet modulates the mass flow, and hence the strength of the jet. Given the initial existence of a small mass appr oximately less than 10(exp -4) M(solar) near the progenitor with a circularization radius approximately 10(exp 10) - 10(exp 11) cm, an una voidable consequence will be the formation of an "external disk" whose outer edge continually moves to larger radii due to angular momentum transport and lack of a confining torque. For long GRBs, if the mass distribution in the initial fall-back disk traces the progenitor envelope, then a radius approximates 10(exp 11) cm gives a time scale app roximately 10(exp 4) s for the X-ray plateau. For late times t > 10(exp 7) s a steepening due to a cooling front in the disk may have obser vational support in GRB 060729. For short GRBs, one expects most of t he mass initially to lie at small radii < 10(exp 8) cm; however the presence of even a trace amount approximately 10(exp -9) M(solar) of hi gh angular material can give a brief plateau in the light curve.

Cannizo, John K.↗

Numerical simulation of the general circulation of the atmosphere of Titan

The atmospheric circulation of Titan is investigated with a general circulation model. The representation of the large-scale dynamics is based on a grid point model developed and used at Laboratoire de Meteorologie Dynamique for climate studies. The code also includes an accurate representation of radiative heating and cooling by molecular gases and haze as well as a parametrization of the vertical turbulent mixing of momentum and potential temperature. Long-term simulations of the atmospheric circulation are presented. Starting from a state of rest, the model spontaneously produces a strong superrotation with prograde equatorial winds (i.e., in the same sense as the assumed rotation of the solid body) increasing from the surface to reach 100 m sec-1 near the 1-mbar pressure level. Those equatorial winds are in very good agreement with some indirect observations, especially those of the 1989 occultation of Star 28-Sgr by Titan. On the other hand, the model simulates latitudinal temperature contrasts in the stratosphere that are significantly weaker than those observed by Voyager 1 which, we suggest, may be partly due to the nonrepresentation of the spatial and temporal variations of the abundances of molecular species and haze. We present diagnostics of the simulated atmospheric circulation underlying the importance of the seasonal cycle and a tentative explanation for the creation and maintenance of the atmospheric superrotation based on a careful angular momentum budget.

NASA Discipline Exobiology↗

A Computational Fluid Dynamics Study of Swirling Flow Reduction by using Anti-vortex Baffle

An anti-vortex baffle is a liquid propellant management device placed adjacent to an outlet of the propellant tank. Its purpose is to substantially reduce or eliminate the formation of free surface dip and vortex, as well as prevent vapor ingestion into the outlet, as the liquid drains out through the flight. To design an effective anti-vortex baffle, Computational Fluid Dynamic (CFD) simulations were undertaken for the NASA Ares I vehicle LOX tank subjected to the simulated flight loads with and without the anti-vortex baffle. The Six Degree-Of-Freedom (6- DOF) dynamics experienced by the Crew Launch Vehicle (CLV) during ascent were modeled by modifying the momentum equations in a CFD code to accommodate the extra body forces from the maneuvering in a non-inertial frame. The present analysis found that due to large moments, the CLV maneuvering has significant impact on the vortical flow generation inside the tank. Roll maneuvering and side loading due to pitch and yaw are shown to induce swirling flow. The vortical flow due to roll is symmetrical with respect to the tank centerline, while those induced by pitch and yaw maneuverings showed two vortices side by side. The study found that without the anti-vortex baffle, the swirling flow caused surface dip during the late stage of drainage and hence early vapor ingestion. The flow can also be non-uniform in the drainage pipe as the secondary swirling flow velocity component can be as high as 10% of the draining velocity. An analysis of the vortex dynamics shows that the swirling flow in the drainage pipe during the Upper Stage burn is mainly the result of residual vortices inside the tank due to conservation of angular momentum. The study demonstrated that the swirling flow in the drainage pipe can be effectively suppressed by employing the anti-vortex baffle.

Yang, H. Q.↗

A Computational Fluid Dynamics Study of Swirling Flow Reduction by Using Anti-Vortex Baffle

An anti-vortex baffle is a liquid propellant management device placed adjacent to an outlet of the propellant tank. Its purpose is to substantially reduce or eliminate the formation of free surface dip and vortex, as well as prevent vapor ingestion into the outlet, as the liquid drains out through the flight. To design an effective anti-vortex baffle, Computational Fluid Dynamic (CFD) simulations were undertaken for the NASA Ares I vehicle LOX tank subjected to the simulated flight loads with and without the anti-vortex baffle. The Six Degree-Of-Freedom (6-DOF) dynamics experienced by the Crew Launch Vehicle (CLV) during ascent were modeled by modifying the momentum equations in a CFD code to accommodate the extra body forces from the maneuvering in a non-inertial frame. The present analysis found that due to large moments, the CLV maneuvering has a significant impact on the vortical flow generation inside the tank. Roll maneuvering and side loading due to pitch and yaw are shown to induce swirling flow. The vortical flow due to roll is symmetrical with respect to the tank centerline, while those induced by pitch and yaw maneuverings showed two vortices side by side. The study found that without the anti-vortex baffle, the swirling flow caused surface dip during the late stage of drainage and hence early vapor ingestion. The flow can also be non-uniform in the drainage pipe as the secondary swirling flow velocity component can be as high as 10% of the draining velocity. An analysis of the vortex dynamics shows that the swirling flow in the drainage pipe during the Upper Stage burn is mainly the result of residual vortices inside the tank due to the conservation of angular momentum. The study demonstrated that the swirling flow in the drainage pipe can be effectively suppressed by employing the anti-vortex baffle.

Yang, H. Q.↗

A Computational Fluid Dynamics Study of Swirling Flow Reduction by Using Anti-Vortex Baffle

An anti-vortex baffle is a liquid propellant management device placed adjacent to an outlet of the propellant tank. Its purpose is to substantially reduce or eliminate the formation of free surface dip and vortex, as well as prevent vapor ingestion into the outlet, as the liquid drains out through the flight. To design an effective anti-vortex baffle, Computational Fluid Dynamic (CFD) simulations were undertaken for the NASA Ares I vehicle LOX tank subjected to the simulated flight loads with and without the anti-vortex baffle. The Six Degree-Of-Freedom (6-DOF) dynamics experienced by the Crew Launch Vehicle (CLV) during ascent were modeled by modifying the momentum equations in a CFD code to accommodate the extra body forces from the maneuvering in a non-inertial frame. The present analysis found that due to large moments, the CLV maneuvering has a significant impact on the vortical flow generation inside the tank. Roll maneuvering and side loading due to pitch and yaw are shown to induce swirling flow. The vortical flow due to roll is symmetrical with respect to the tank centerline, while those induced by pitch and yaw maneuverings showed two vortices side by side. The study found that without the anti-vortex baffle, the swirling flow caused surface dip during the late stage of drainage and hence early vapor ingestion. The flow can also be non-uniform in the drainage pipe as the secondary swirling flow velocity component can be as high as 10% of the draining velocity. An analysis of the vortex dynamics shows that the swirling flow in the drainage pipe during the Upper Stage burn is mainly the result of residual vortices inside the tank due to the conservation of angular momentum. The study demonstrated that the swirling flow in the drainage pipe can be effectively suppressed by employing the anti-vortex baffle.

Yang, H. Q.↗

Inner Core Rotation from Geomagnetic Westward Drift and a Stationary Spherical Vortex in Earth's Core

The idea that geomagnetic westward drift indicates convective leveling of the planetary momentum gradient within Earth's core is pursued in search of a differentially rotating mean state, upon which various oscillations and secular effects might be superimposed. The desired state conforms to roughly spherical boundary conditions, minimizes dissipative interference with convective cooling in the bulk of the core, yet may aid core cooling by depositing heat in the uppermost core and lower mantle. The variational calculus of stationary dissipation applied to a spherical vortex within the core yields an interesting differential rotation profile, akin to spherical Couette flow bounded by thin Hartmann layers. Four boundary conditions are required. To concentrate shear induced dissipation near the core-mantle boundary, these are taken to be: (i) no-slip at the core-mantle interface; (ii) geomagnetically estimated bulk westward flow at the base of the core-mantle boundary layer; (iii) no-slip at the inner-outer core interface; and, to describe magnetic locking of the inner core to the deep outer core; (iv) hydrodynamically stress-free at the inner-outer core boundary. By boldly assuming the axial core angular momentum anomaly to be zero, the super-rotation of the inner core relative to the mantle is calculated to be at most 1.5 deg./yr.

Voorhies, Coerte V.↗

Inner Core Rotation from Geomagnetic Westward Drift and a Stationary Spherical Vortex in Earth's Core

The idea that geomagnetic westward drift indicates convective leveling of the planetary momentum gradient within Earth's core is pursued in search of a differentially rotating mean state, upon which various oscillations and secular effects might be superimposed. The desired state conforms to roughly spherical boundary conditions, minimizes dissipative interference with convective cooling in the bulk of the core, yet may aide core cooling by depositing heat in the uppermost core and lower mantle. The variational calculus of stationary dissipation applied to a spherical vortex within the core yields an interesting differential rotation profile akin to spherical Couette flow bounded by thin Hartmann layers. Four boundary conditions are required. To concentrate shear induced dissipation near the core-mantle boundary, these are taken to be: (i) no-slip at the core-mantle interface; (ii) geomagnetically estimated bulk westward flow at the base of the core-mantle boundary layer; (iii) no-slip at the inner-outer core interface; and, to describe magnetic locking of the inner core to the deep outer core, (iv) hydrodynamically stress-free at the inner-outer core boundary. By boldly assuming the axial core angular momentum anomaly to be zero, the super-rotation of the inner core is calculated to be at most 1.5 degrees per year.

Voorhies, C. V.↗