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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Topological classification of the Goryachev integrable case in rigid body dynamics

A topological analysis of the Goryachev integrable case in rigid body dynamics is made on the basis of the Fomenko-Zieschang theory. The invariants (marked molecules) which are obtained give a complete description, from the standpoint of Liouville classification, of the systems of Goryachev type on various level sets of the energy. It turns out that on appropriate energy levels the Goryachev case is Liouville equivalent to many classical integrable systems and, in particular, the Joukowski, Clebsch, Sokolov and Kovalevskaya-Yehia cases in rigid body dynamics, as well as to some integrable billiards in plane domains bounded by confocal quadrics -- in other words, the foliations given by the closures of generic solutions of these systems have the same structure. Bibliography: 15 titles.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2004

Hamilton's Equations with Euler Parameters for Rigid Body Dynamics Modeling

A combination of Euler parameter kinematics and Hamiltonian mechanics provides a rigid body dynamics model well suited for use in strongly nonlinear problems involving arbitrarily large rotations. The model is unconstrained, free of singularities, includes a general potential energy function and a minimum set of momentum variables, and takes an explicit state space form convenient for numerical implementation. The general formulation may be specialized to address particular applications, as illustrated in several three dimensional example problems.

Shivarama, Ravishankar↗
DOE OSTI2014

The phase topology of a special case of Goryachev integrability in rigid body dynamics

The phase topology of a special case of Goryachev integrability in the problem of motion of a rigid body in a fluid is investigated using the method of Boolean functions, which was developed by Kharlamov for algebraically separated systems. The bifurcation diagram of the moment map is found and the Fomenko invariant, which classifies the systems up to rough Liouville equivalence, is specified. Bibliography: 15 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I

In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In conclusion, these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part II

Here, in this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

A discrete momentum-conserving explicit algorithm for rigid body dynamics analysis

A discrete momentum-conserving explicit time integration is presented. The accurate feature and simplicity of the present algorithm are realized by a mid-point implicit formula for integrating the Euler parameters and a second-order discrete momentum-conserving form of the central difference algorithm, respectively. The accuracy and robustness of the algorithm is demonstrated by example problems which exhibit large overall rigid motions under holonomic constraints.

Park, K. C.↗
NASA NTRS2011

Computational Fluid Dynamics Demonstration of Rigid Bodies in Motion

The Design Analysis Branch (NE-Ml) at the Kennedy Space Center has not had the ability to accurately couple Rigid Body Dynamics (RBD) and Computational Fluid Dynamics (CFD). OVERFLOW-D is a flow solver that has been developed by NASA to have the capability to analyze and simulate dynamic motions with up to six Degrees of Freedom (6-DOF). Two simulations were prepared over the course of the internship to demonstrate 6DOF motion of rigid bodies under aerodynamic loading. The geometries in the simulations were based on a conceptual Space Launch System (SLS). The first simulation that was prepared and computed was the motion of a Solid Rocket Booster (SRB) as it separates from its core stage. To reduce computational time during the development of the simulation, only half of the physical domain with respect to the symmetry plane was simulated. Then a full solution was prepared and computed. The second simulation was a model of the SLS as it departs from a launch pad under a 20 knot crosswind. This simulation was reduced to Two Dimensions (2D) to reduce both preparation and computation time. By allowing 2-DOF for translations and 1-DOF for rotation, the simulation predicted unrealistic rotation. The simulation was then constrained to only allow translations.

Camarena, Ernesto↗
NASA NTRS1990

Direct inversion of rigid-body rotational dynamics

The global linearization (inversion) of rigid-body rotational dynamics is reviewed and representations in terms of quaternions and direction cosines are compared. Certain properties common to quaternions and direction cosines that make their use preferable to Euler angles and that simplify the inversion procedure are described. Applications of the inversion procedure for state estimation and attitude control are discussed. To avoid complexities caused by aerodynamics, an example of direct inversion for linear feedback control of spacecraft attitude is given.

Bach, Ralph↗
NASA NTRS1990

Direct inversion of rigid-body rotational dynamics

The global linearization (inversion) of rigid-body rotational dynamics is reviewed, and representations in terms of quaternions and direction cosines are compared. Certain properties common to quaternions and direction cosines that make their use preferable to Euler angles and that simplify the inversion procedure are described. Applications of the inversion procedure for state estimation and attitude control are discussed. To avoid complexities caused by aerodynamics, an example of direct inversion for linear feedback control of spacecraft attitude is given.

Bach, Ralph↗
NASA NTRS1992

Three-dimensional simulation of slender delta wing rock and divergence

Computational simulation of three-dimensional flows around a delta wing undergoing rock and roll-divergence motions is presented. The problem is a multidisciplinary one where fluid-dynamics equations and rigid-body-dynamics equations are sequentially solved. For the fluid-dynamics part, the unsteady Euler equations, which are written relative to a moving frame of reference, are solved using an implicit, approximately-factored, central-difference, finite-volume scheme. For the rigid-body dynamics part, the Euler equation of rigid-body rolling motion is solved using a four-stage Runge-Kutta scheme. Since the applications do not include deforming wings or relative-rigid-body motions, the computational-fluid-dynamics grid, which is fixed in the moving frame of reference, does not need to be updated once it is generated.

Kandil, Osama A.↗
NASA NTRS1995

Methodology for simulation of unsteady flows to determine the time-dependent interference between stationary and moving boundaries

A new methodology is developed to simulate unsteady flows about prescribed and aerodynamically determined moving boundary problems. The method couples the fluid dynamics and rigid-body dynamics equations to capture the time-dependent interference between stationary and moving boundaries. The unsteady, compressible, inviscid (Euler) equations are solved on dynamic, unstructured grids by an explicit, finite-volume, upwind method. For efficiency, the grid adaptation is performed within a window around the moving object. The Eulerian equations of the rigid-body dynamics are solved by a Runge-Kutta method in a non-inertial frame of reference. The two-dimensional flow solver is validated by computing the flow past a sinusoidally-pitching airfoil and comparing these results with the experimental data. The overall methodology is used for two two-dimensional examples: the flow past an airfoil which is performing a three-degrees-of-freedom motion in a transonic freestream, and the free-fall of a store after separation from a wing-section. Then the unstructured mesh methodology is extended to three-dimensions to simulate unsteady flow past bodies in relative motion, where the trajectory is determined from the instantaneous aerodynamics. The flow solver and the adaptation scheme in three dimensions are validated by simulating the transonic, unsteady flow around a wing undergoing a forced, periodic, pitching motion, and comparing the results with the experimental data. To validate the trajectory code, the six-degrees-of-freedom motion of a store separating from a wing was computed using the experimentally determined force and moment fields, then comparing with an independently generated trajectory. Finally, the overall methodology was demonstrated by simulating the unsteady flowfield and the trajectory of a store dropped from a wing. The methodology, its computational cost notwithstanding, has proven to be accurate, automated, easy for dynamic gridding, and relatively efficient for the required man-hours.

Singh, Kamakhya Prasad↗
NASA NTRS1994

Predicting the effects of unmodeled dynamics on an aircraft flight control system design using eigenspace assignment

When using eigenspace assignment to design an aircraft flight control system, one must first develop a model of the plant. Certain questions arise when creating this model as to which dynamics of the plant need to be included in the model and which dynamics can be left out or approximated. The answers to these questions are important because a poor choice can lead to closed-loop dynamics that are unpredicted by the design model. To alleviate this problem, a method has been developed for predicting the effect of not including certain dynamics in the design model on the final closed-loop eigenspace. This development provides insight as to which characteristics of unmodeled dynamics will ultimately affect the closed-loop rigid-body dynamics. What results from this insight is a guide for eigenstructure control law designers to aid them in determining which dynamics need or do not need to be included and a new way to include these dynamics in the flight control system design model to achieve a required accuracy in the closed-loop rigid-body dynamics. The method is illustrated for a lateral-directional flight control system design using eigenspace assignment for the NASA High Alpha Research Vehicle (HARV).

Johnson, Eric N.↗
NASA NTRS1991

Effects of leading-edge flap oscillation on unsteady delta wing flow and rock control

The isolated and interdisciplinary problems of unsteady fluid dynamics and rigid-body dynamics and control of delta wings with and without leading-edge flap oscillation are considered. For the fluid dynamics problem, the unsteady, compressible, thin-layer Navier-Stokes (NS) equations, which are written relative to a moving frame of reference, are solved along with the unsteady, linearized, Navier-displacement (ND) equations. The NS equations are solved for the flowfield using an implicit finite-volume scheme. The ND equations are solved for the grid deformation, if the leading-edge flaps oscillate, using an ADI scheme. For the dynamics and control problem, the Euler equation of rigid-body rolling motion for a wing and its flaps are solved interactively with the fluid dynamics equations for the wing-rock motion and subsequently for its control. A four-stage Runge-Kutta scheme is used to explicitly integrate the dynamics equation.

Kandil, Osama A.↗
DOE OSTI2015

Parameterized Receptacle-Pin Contact Model

This report describes a simple, quasi-static, closed-form, parameterized model that predicts the contact forces acting between axially-engaging electrical contact receptacles and a pin. This approach is useful for design studies and reduced-order mechanism modeling, where receptacle-pin insertion forces have traditionally been difficult to quantify without high-fidelity (e.g. rigid body dynamics, finite element analysis) simulations. A Matlab implementation of the model is provided and is demonstrated for three receptacle geometries. Results are compared to rigid body dynamics simulations for the first two geometries and experimental insertion force measurements for the third.

42 ENGINEERING↗
DOE OSTI2014

Development of an improved MATLAB GUI for the prediction of coefficients of restitution, and integration into LMS.

In 2012, a Matlab GUI for the prediction of the coefficient of restitution was developed in order to enable the formulation of more accurate Finite Element Analysis (FEA) models of components. This report details the development of a new Rebound Dynamics GUI, and how it differs from the previously developed program. The new GUI includes several new features, such as source and citation documentation for the material database, as well as a multiple materials impact modeler for use with LMS Virtual.Lab Motion (LMS VLM), and a rigid body dynamics modeling software. The Rebound Dynamics GUI has been designed to work with LMS VLM to enable straightforward incorporation of velocity-dependent coefficients of restitution in rigid body dynamics simulations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1997

Effective Control of Computationally Simulated Wing Rock in Subsonic Flow

The unsteady compressible, full Navier-Stokes (NS) equations and the Euler equations of rigid-body dynamics are sequentially solved to simulate the delta wing rock phenomenon. The NS equations are solved time accurately, using the implicit, upwind, Roe flux-difference splitting, finite-volume scheme. The rigid-body dynamics equations are solved using a four-stage Runge-Kutta scheme. Once the wing reaches the limit-cycle response, an active control model using a mass injection system is applied from the wing surface to suppress the limit-cycle oscillation. The active control model is based on state feedback and the control law is established using pole placement techniques. The control law is based on the feedback of two states: the roll-angle and roll velocity. The primary model of the computational applications consists of a 80 deg swept, sharp edged, delta wing at 30 deg angle of attack in a freestream of Mach number 0.1 and Reynolds number of 0.4 x 10(exp 6). With a limit-cycle roll amplitude of 41.1 deg, the control model is applied, and the results show that within one and one half cycles of oscillation, the wing roll amplitude and velocity are brought to zero.

Kandil, Osama A.↗
NASA NTRS2010

Modeling Attitude Dynamics in Simulink: A Study of the Rotational and Translational Motion of a Spacecraft Given Torques and Impulses Generated by RMS Hand Controllers

In order to study and control the attitude of a spacecraft, it is necessary to understand the natural motion of a body in orbit. Assuming a spacecraft to be a rigid body, dynamics describes the complete motion of the vehicle by the translational and rotational motion of the body. The Simulink Attitude Analysis Model applies the equations of rigid body motion to the study of a spacecraft?s attitude in orbit. Using a TCP/IP connection, Matlab reads the values of the Remote Manipulator System (RMS) hand controllers and passes them to Simulink as specified torque and impulse profiles. Simulink then uses the governing kinematic and dynamic equations of a rigid body in low earth orbit (LE0) to plot the attitude response of a spacecraft for five seconds given known applied torques and impulses, and constant principal moments of inertia.

Mauldin, Rebecca H.↗
NASA NTRS2015

Airborne Simulation of Launch Vehicle Dynamics

In this paper we present a technique for approximating the short-period dynamics of an exploration-class launch vehicle during flight test with a high-performance surrogate aircraft in relatively benign endoatmospheric flight conditions. The surrogate vehicle relies upon a nonlinear dynamic inversion scheme with proportional-integral feedback to drive a subset of the aircraft states into coincidence with the states of a time-varying reference model that simulates the unstable rigid body dynamics, servodynamics, and parasitic elastic and sloshing dynamics of the launch vehicle. The surrogate aircraft flies a constant pitch rate trajectory to approximate the boost phase gravity turn ascent, and the aircraft's closed-loop bandwidth is sufficient to simulate the launch vehicle's fundamental lateral bending and sloshing modes by exciting the rigid body dynamics of the aircraft. A novel control allocation scheme is employed to utilize the aircraft's relatively fast control effectors in inducing various failure modes for the purposes of evaluating control system performance. Sufficient dynamic similarity is achieved such that the control system under evaluation is configured for the full-scale vehicle with no changes to its parameters, and pilot-control system interaction studies can be performed to characterize the effects of guidance takeover during boost. High-fidelity simulation and flight-test results are presented that demonstrate the efficacy of the design in simulating the Space Launch System (SLS) launch vehicle dynamics using the National Aeronautics and Space Administration (NASA) Armstrong Flight Research Center Fullscale Advanced Systems Testbed (FAST), a modified F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois), over a range of scenarios designed to stress the SLS's Adaptive Augmenting Control (AAC) algorithm.

airborne simulation↗