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NASA NTRSDate not supplied

A UNIQUE APPROACH TO ACHIEVING SIZE-CONSTRAINED QUASI-HALO ORBITS FOR THE ROMAN SPACE TELESCOPE

The Nancy Grace Roman Space Telescope (RST) is an infrared space observatory planned for launch in the mid-2020’s. The launch window design for RST is subject to a wide variety of simultaneous requirements that require careful consideration and control of mission orbits and the trajectories used to achieve them. This work describes an innovative methodology that blends classical methods with modern manifold approaches and numerical optimization to flexibly determine optimal transfers to desriable mission orbits for any day of the year.Solutions found with this highly automated strategy are gaurunteed to meet requirements by construction. Results show that RST can launch for 80% of the year using maneuvers that are well within the fuel budget, significantly reducing cost and risk to the mission

Lauren Schlenker↗

NASA NTRS2014

Bifurcation Analysis Using Rigorous Branch and Bound Methods

For the study of nonlinear dynamic systems, it is important to locate the equilibria and bifurcations occurring within a specified computational domain. This paper proposes a new approach for solving these problems and compares it to the numerical continuation method. The new approach is based upon branch and bound and utilizes rigorous enclosure techniques to yield outer bounding sets of both the equilibrium and local bifurcation manifolds. These sets, which comprise the union of hyper-rectangles, can be made to be as tight as desired. Sufficient conditions for the existence of equilibrium and bifurcation points taking the form of algebraic inequality constraints in the state-parameter space are used to calculate their enclosures directly. The enclosures for the bifurcation sets can be computed independently of the equilibrium manifold, and are guaranteed to contain all solutions within the computational domain. A further advantage of this method is the ability to compute a near-maximally sized hyper-rectangle of high dimension centered at a fixed parameter-state point whose elements are guaranteed to exclude all bifurcation points. This hyper-rectangle, which requires a global description of the bifurcation manifold within the computational domain, cannot be obtained otherwise. A test case, based on the dynamics of a UAV subject to uncertain center of gravity location, is used to illustrate the efficacy of the method by comparing it with numerical continuation and to evaluate its computational complexity.

Smith, Andrew P.↗

NASA NTRS1989

On an efficient and accurate method to integrate restricted three-body orbits

This work is a quantitative analysis of the advantages of the Bulirsch-Stoer (1966) method, demonstrating that this method is certainly worth considering when working with small N dynamical systems. The results, qualitatively suspected by many users, are quantitatively confirmed as follows: (1) the Bulirsch-Stoer extrapolation method is very fast and moderately accurate; (2) regularization of the equations of motion stabilizes the error behavior of the method and is, of course, essential during close approaches; and (3) when applicable, a manifold-correction algorithm reduces numerical errors to the limits of machine accuracy. In addition, for the specific case of the restricted three-body problem, even a small eccentricity for the orbit of the primaries drastically affects the accuracy of integrations, whether regularized or not; the circular restricted problem integrates much more accurately.

Murison, Marc A.↗

NASA NTRS1988

Numerical simulation methods of incompressible flows and an application to the space shuttle main engine

Incompressible Navier-Stokes solution methods are discussed with an emphasis on the pseudocompressibility method. A steady-state flow solver based on the pseudocompressibility approach is then described. This flow-solver code was used to analyze the internal flow in the Space Shuttle main engine hot-gas manifold. Salient features associated with this three-dimensional realistic flow simulation are discussed. Numerical solutions relevant to the current engine analysis and the redesign effort are discussed along with experimental results. This example demonstrates the potential of computational fluid dynamics as a design tool for aerospace applications.

Chang, J. L. C.↗

NASA NTRS1988

Numerical simulation methods of incompressible flows and an application to the Space Shuttle main engine

This paper discusses incompressible Navier-Stokes solution methods with an emphasis on the pseudocompressibility method. A steady-state flow solver based on the pseudocompressibility approach is then described. This flow solver code has been used to analyze the internal flow in the Space Shuttle main engine hot-gas manifold. Salient features associated with this three-dimensional realistic flow simulation are discussed. Numerical solutions relevant to the current engine analysis and the redesign effort are discussed along with experimental results. This example demonstrates the potential of computational fluid dynamics as a design tool for aerospace applications.

Chang, J. L. C.↗

NASA NTRS1985

Parametric Stiffness Control of Flexible Structures

An unconventional method for control of flexible space structures using feedback control of certain elements of the stiffness matrix is discussed. The advantage of using this method of configuration control is that it can be accomplished in practical structures by changing the initial stress state in the structure. The initial stress state can be controlled hydraulically or by cables. The method leads, however, to nonlinear control equations. In particular, a long slender truss structure under cable induced initial compression is examined. both analytical and numerical analyses are presented. Nonlinear analysis using center manifold theory and normal form theory is used to determine criteria on the nonlinear control gains for stable or unstable operation. The analysis is made possible by the use of the exact computer algebra system MACSYMA.

Moon, F. C.↗

NASA NTRS1980

A simulation of the atmospheric cloud physics laboratory to aid in its design and the design of the experiments within the laboratory

Using the finite difference method with overrelaxation, numerical solutions of the steady-state vorticity transport equation were obtained for a continuous flow diffusion chamber of the Hudson-Squires type. The calculation neglected the effects due to temperature, gravity, and saturation. The size and shape of the manifold used to inject the aerosol laden flow were varied to obtain a design which would improve the performance of the chamber from strictly low Reynolds number (less than 20) fluid dynamical considerations.

Winchester, L. W., Jr.↗

NASA NTRSDate not supplied

Cislunar Trajectory Design and Maneuver Autonomy for NASA's Moon to Mars Architecture

NASA’s Moon to Mars architecture is an ambitious roadmap of manned cislunar and deep space exploration. The extensive amount of orbital assets required will place a significant burden on ground-based resources, such as communication networks and operations facilities. Spacecraft autonomy is essential for maintaining a vast number of complex missions beyond Earth orbit. To achieve full autonomy, spacecraft must be able to employ methods of robust maneuver design without an explicit dependence on commands sent from the ground. This level of autonomy is needed not only for stationkeeping, but also for outbound transfers. To address the need of spacecraft maneuver design autonomy, this work investigates the use of neural networks (NNs) in a supervised learning environment. A supervised learning approach for NNs allows for a curated training data set, consisting exclusively of perturbations applied to a desired mission concept of operations (ConOps). The proposed approach allows humans on the ground to design a specific mission ConOps before flight, then employ NNs to fly the mission robustly and autonomously. This investigation numerically tests maneuver autonomy in four highly sensitive regions of flight: orbit raising, translunar injection burns, powered lunar flybys, and invariant manifold insertion burns. These straining cases are contextualized by testing them in a demonstration mission, targeting an Earth-Moon L3 orbit. The study first establishes feasibility by automating impulsive burn maneuvers. However, some guidance algorithms will need more intensive commands, such as inertial pointing and angular rates. To validate this method, NN maneuver autonomy is applied to a finite burn model of the demonstration mission. The use of sequential, mission specific maneuvers provide an appropriate testbed to demonstrate the robustness of a NN trained on feasible perturbed states. Moreover, these scenarios provide preliminary proof-of-concept for fully autonomous missions that execute maneuvers without dependence upon explicit command uplinks. As a result, the technological advancement proposed in this work may significantly ease the strain on ground-based mission operations. This would enable complex and autonomous mission execution in cislunar and deep space regimes, filling a technology gap required to support future manned missions.

NASA↗

NASA NTRS1987

Numerical simulation of flow path in the oxidizer side hot gas manifold of the Space Shuttle main engine

The purpose of this study is to examine in detail incompressible laminar and turbulent flows inside the oxidizer side Hot Gas Manifold of the Space Shuttle Main Engine. To perform this study, an implicit finite difference code cast in general curvilinear coordinates is further developed. The code is based on the method of pseudo-compressibility and utilize ADI or implicit approximate factorization algorithm to achieve computational efficiency. A multiple-zone method is developed to overcome the complexity of the geometry. In the present study, the laminar and turbulent flows in the oxidizer side Hot Gas Manifold have been computed. The study reveals that: (1) there exists large recirculation zones inside the bowl if no vanes are present; (2) strong secondary flows are observed in the transfer tube; and (3) properly shaped and positioned guide vanes are effective in eliminating flow separation.

Lin, S. J.↗

NASA NTRS1985

Numerical analysis of flow non-uniformity in the hot gas manifold of the Space Shuttle main engine

Three-dimensional viscous flow in a conceptual hot gas manifold (HGM) for the Space Shuttle Main Engine High Pressure Fuel Turbopump (SSME HPFTP) was numerically analyzed. A finite difference scheme was used to solve the Navier-Stokes equations. The exact geometry of the SSME HGM was modeled using boundary fitted curvilinear coordinates and the General Interpolants Method (GIM) code. Slight compressibility of the subsonic flow was modeled using a linearized equation of state with artificial compressibility. A time relaxation method was used to obtain a steady state solution. The feasibility and potential usefulness of computational methods in assisting the design of SSME components which involves the flow of fluids within complex geometrical shapes is demonstrated.

Thoenes, J.↗

NASA NTRS1965

Studies in Perturbation Theory. XI. Lower Bounds to Energy Eigenvalues, Ground State, and Excited States

The bracketing theorem in the partitioning technique for solving the Schrödinger equation may be used in principle to determine upper and lower bounds to energy eigenvalues. Practical lower bounds of any accuracy desired may be evaluated by utilizing the properties of ``inner projections'' on finite manifolds in the Hilbert space. The method is here applied to the ground state and excited states of a Hamiltonian H=H(sub 0)+V having a positive definite perturbation V. Even if inspiration is derived from the method of intermediate Hamiltonians, the final results are of bracketing type and independent of this approach. The method is numerically illustrated in some accompanying papers.

Loewdin, Per-Olov↗

NASA NTRS1993

Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.

Vaughan, William W.↗

NASA NTRSDate not supplied

Evolution of Astrodynamics for Multibody Environments, Numerical Precision and Dynamical Understanding

The innovative nature of dynamical systems theory and its applications in trajectory design enabled many recent missions by opening up new transfer and capture opportunities to meet mission requirements, reduce fuel costs, and address various launch constraints and contingencies. With a combination of proven numerical methods and an advanced understanding of the dynamics, an ‘experienced’ user can rapidly design multibody and cislunar missions such as Lunar IceCube and Artemis/Themis and relatively quickly conceive trajectory concepts for Sun-Earth mission orbits, such as the Space Weather Follow On-L1 Lissajous orbit—one that can be achieved and maintained.

Dynamical Systems↗

NASA NTRS1994

Topological analysis of chaotic orbits: Revisiting Hyperion

There is emerging interest in the possibility of chaotic evolution in astrophysical systems. To mention just one example, recent well-sampled ground-based observations of the Saturian satellite Hyperion strongly suggest that it is exhibiting chaotic behavior. We present a general technique, the method of close returns, for the analysis of data from astronomical objects believed to be exhibiting chaotic motion. The method is based on the extraction of pieces of the evolution that exhibit nearly periodic behavior-episodes during which the object stays near in phase space to some unstable periodic orbit. Such orbits generally act as skeletal features, tracing the topological organization of the manifold on which the chaotic dynamics takes place. This method does not require data sets as lengthy as other nonlinear analysis techniques do and is therefore well suited to many astronomical observing programs. Well sampled data covering between twenty and forty characteristic periods of the system have been found to be sufficient for the application of this technique. Additional strengths of this method are its robustness in the presence of noise and the ability for a user to clearly distinguish between periodic, random, and chaotic behavior by inspection of the resulting two-dimensional image. As an example of its power, we analyze close returns in a numerically generated data set, based on a model for Hyperion extensively studied in the literature, corresponding to nightly observations of the satellite. We show that with a small data set, embedded unstable periodic orbits can be extracted and that these orbits can be responsible for nearly periodic behavior lasting a substantial fraction of the observing run.

Boyd, Patricia T.↗

NASA NTRS2012

Progress Toward Affordable High Fidelity Combustion Simulations Using Filtered Density Functions for Hypersonic Flows in Complex Geometries

Significant progress has been made in the development of subgrid scale (SGS) closures based on a filtered density function (FDF) for large eddy simulations (LES) of turbulent reacting flows. The FDF is the counterpart of the probability density function (PDF) method, which has proven effective in Reynolds averaged simulations (RAS). However, while systematic progress is being made advancing the FDF models for relatively simple flows and lab-scale flames, the application of these methods in complex geometries and high speed, wall-bounded flows with shocks remains a challenge. The key difficulties are the significant computational cost associated with solving the FDF transport equation and numerically stiff finite rate chemistry. For LES/FDF methods to make a more significant impact in practical applications a pragmatic approach must be taken that significantly reduces the computational cost while maintaining high modeling fidelity. An example of one such ongoing effort is at the NASA Langley Research Center, where the first generation FDF models, namely the scalar filtered mass density function (SFMDF) are being implemented into VULCAN, a production-quality RAS and LES solver widely used for design of high speed propulsion flowpaths. This effort leverages internal and external collaborations to reduce the overall computational cost of high fidelity simulations in VULCAN by: implementing high order methods that allow reduction in the total number of computational cells without loss in accuracy; implementing first generation of high fidelity scalar PDF/FDF models applicable to high-speed compressible flows; coupling RAS/PDF and LES/FDF into a hybrid framework to efficiently and accurately model the effects of combustion in the vicinity of the walls; developing efficient Lagrangian particle tracking algorithms to support robust solutions of the FDF equations for high speed flows; and utilizing finite rate chemistry parametrization, such as flamelet models, to reduce the number of transported reactive species and remove numerical stiffness. This paper briefly introduces the SFMDF model (highlighting key benefits and challenges), and discusses particle tracking for flows with shocks, the hybrid coupled RAS/PDF and LES/FDF model, flamelet generated manifolds (FGM) model, and the Irregularly Portioned Lagrangian Monte Carlo Finite Difference (IPLMCFD) methodology for scalable simulation of high-speed reacting compressible flows.

Drozda, Tomasz G.↗

NASA NTRS1987

Nonlinear dynamics of attractive magnetic bearings

The nonlinear dynamics of a ferromagnetic shaft suspended by the force of attraction of 1, 2, or 4 independent electromagnets is presented. Each model includes a state variable feedback controller which has been designed using the pole placement method. The constitutive relationships for the magnets are derived analytically from magnetic circuit theory, and the effects of induced eddy currents due to the rotation of the journal are included using Maxwell's field relations. A rotor suspended by four electro-magnets with closed loop feedback is shown to have nine equilibrium points within the bearing clearance space. As the rotor spin speed increases, the system is shown to pass through a Hopf bifurcation (a flutter instability). Using center manifold theory, this bifurcation can be shown to be of the subcritical type, indicating an unstable limit cycle below the critical speed. The bearing is very sensitive to initial conditions, and the equilibrium position is easily upset by transient excitation. The results are confirmed by numerical simulation.

Hebbale, K. V.↗

NASA NTRSDate not supplied

Fluid & Thermal Analysis of a Manifold Microchannel Heat Sink

A three-dimensional (3-D) numerical model has been developed to study the fluid flow and heat transfer through a manifold-microchannel (MMC) heat sink, a microfluidic cooling system designed as a heat dissipation solution for compact, high-powered electronic systems. An MMC consists of a 3-D manifold structure that distributes working fluid through alternating inlet and outlet manifold channels that guide the fluid to and from the microchannels, shortening the flow length and thereby, reducing the pressure drop across the system. Wide bandgap semiconductors such as silicon carbide (SiC) are increasingly utilized due to their ability to enable smaller electronic devices and components to operate more efficiently at higher frequencies. These semiconductors can greatly benefit from the MMC, which can extract all the heat produced by compact, high-powered electronics, enabling them to achieve optimal performance. The MMC also utilizes an embedded cooling approach which allows for fabrication directly within SiC-based electronics, resulting in significant mass and weight savings and lower thermal resistance than conventional heat sink designs. This paper outlines the methods used to conduct fluid and thermal analysis of different MMC configurations for flow parameters such as flow rate and inlet flow conditions. This study involves both steady state and transient thermal analysis as a gradually increasing heat flux is applied to the system over time, which is representative of the heat dissipation from the electronics over a given period. Results from the analysis show that the MMC is capable of effectively dissipating heat flux of ~100 W/cm2 while maintaining considerably low pressure drop (< 1 kPa) and thermal resistance (< 1 K/W) for certain single-phase working fluids.

manifold microchannel↗

NASA NTRSDate not supplied

Fluid & Thermal Analysis of a Manifold Microchannel Heat Sink

manifold microchannel↗