The Invariant Manifolds and Solar System Dynamics
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solar system dynamics invariant manifolds three bo↗
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Stability maps, unstable periodic orbits and transfers in the Jovian system
Low cost transfers of a spacecraft in a multi-gravitational orbital environment, which are based on connections between unstable periodic orbits, present several trade-offs, such time-of-flight v.s transfer fuel cost.
low-cost transfers↗
The role of invariant manifolds in lowthrust trajectory design (part III)
This paper is the third in a series to explore the role of invariant manifolds in the design of low thrust trajectories. In previous papers, we analyzed an impulsive thrust resonant gravity assist flyby trajectory to capture into Europa orbit using the invariant manifolds of unstable resonant periodic orbits and libration orbits. The energy savings provided by the gravity assist may be interpreted dynamically as the result of a finite number of intersecting invariant manifolds. In this paper we demonstrate that the same dynamics is at work for low thrust trajectories with resonant flybys and low energy capture. However, in this case, the flybys and capture are effected by continuous families of intersecting invariant manifolds.
low thrust trajectories↗
The interplanetary superhighway and human habitation on the Moon
NASA's new vision to return humans to the Moon is the next practical step in expanding human habitation beyond Earth. As the Habitation 2006 Conference website states: 'new knowledge and new technologies are required.' Along with the development of new habitation systems, an important consideration is how to transport these heavy structures cheaply to the Moon? We propose the use of ultra-low-energy orbits in the Interplanetary Superhighway as an economical and effective means to deliver cargo to the Moon. This approach not only reduces the propulsion cost, but also provides enormous flexibility and robustness to the mission architecture.
Jupiter Icy Moons Orbiter (JIMO)↗
Surface structure of an invariant manifold of a Halo Orbit (extended abstract)
We extract the surface structure of the unstable invariant manifold tube projected into position space, of a halo orbit near L2. We do this by using transversal planes to intersect trajectories that approximate the tube. From these intersection points we construct spline-interpolated cross section curves which give a good idea of the structure of the tube. For example, we show that, for the value of (mu) we use, the tube pinches, develops a self-intersection, develops loop-inside-tube structure, pinches some more, and so on. We also construct surfaces made of quadrilaterals and triangles from these cross-sections. The transversal planes are obtained by taking planes orthogonal to a curve that follows the general shape of the tube. One such curve we use, is the unstable invariant manifold of the equilibrium point L2 itself. In another example, we take a circle that follows the tube, as the curve for finding planes transversal to the tube. Our method is complementary to the method of taking cross-sections of constant time (the isochronous method), as used by some other researchers. The isochronous method is good at revealing the temporal structure of trajectories on a tube. However, due to the unequal speeds of different trajectories, it is harder to use for long length surface extraction. In contrast, using our method, we show cross-sections of the tube through an angular extent of nearly (pi) during which the tube becomes extremely convoluted. We also show that tubes of different energies, that start out in certain ordering, do not obey the ordering after a while. Our work is motivated by applications to space mission design.
invariant manifold↗
Effect of Flow Incidence and Reynolds Number on Low-Speed Aerodynamic Characteristics of Several Noncircular Cylinders with Applications to Directional Stability and Spinning
The aerodynamic characteristics of several noncircular two-dimensional cylinders with axes normal to the stream at various flow incidences (analogous to angles of attack of a two-dimensional airfoil and obtained by rotating the cylinders about their axes) for a range of Reynolds numbers have been determined from low-speed wind-tunnel tests. The results indicate that these parameters have rather large effects on the drag and side force developed on these cylinders. The side force is especially critical and very often undergoes a change in sign with a change in Reynolds number. Since the flow incidences correspond to combined angles of attack and sideslip in the crossflow plane of three-dimensional bodies, these two-dimensional results appear to have strong implications with regard to directional stability of fuselages at high angles of attack. These implications, along with those associated with the spin-recovery characteristics of aircraft, are briefly discussed.
Polhamus, Edward C.↗
Optimizing Spacecraft Placement for Liaison Constellations
A navigation and communications network is proposed to support an anticipated need for infrastructure in the Earth-Moon system. Periodic orbits will host the constellations while a novel, autonomous navigation strategy will guide the spacecraft along their path strictly based on satellite-to-satellite telemetry. In particular, this paper investigates the second stage of a larger constellation optimization scheme for multi-spacecraft systems. That is, following an initial orbit down-selection process, this analysis provides insights into the ancillary problem of spacecraft placement. Two case studies are presented that consider configurations of up to four spacecraft for a halo orbit and a cycler trajectory.
lunar cycler orbits↗
Applying Dynamical Systems Theory to Optimize Libration Point Orbit Stationkeeping Maneuvers for WIND
NASA's WIND mission has been operating in a large amplitude Lissajous orbit in the vicinity of the interior libration point of the Sun-Earth/Moon system since 2004. Regular stationkeeping maneuvers are required to maintain the orbit due to the instability around the collinear libration points. Historically these stationkeeping maneuvers have been performed by applying an incremental change in velocity, or (delta)v along the spacecraft-Sun vector as projected into the ecliptic plane. Previous studies have shown that the magnitude of libration point stationkeeping maneuvers can be minimized by applying the (delta)v in the direction of the local stable manifold found using dynamical systems theory. This paper presents the analysis of this new maneuver strategy which shows that the magnitude of stationkeeping maneuvers can be decreased by 5 to 25 percent, depending on the location in the orbit where the maneuver is performed. The implementation of the optimized maneuver method into operations is discussed and results are presented for the first two optimized stationkeeping maneuvers executed by WIND.
WIND↗
Low-Energy Ballistic Transfers to Lunar Halo Orbits
Recent lunar missions have begun to take advantage of the benefits of low-energy ballistic transfers between the Earth and the Moon rather than implementing conventional Hohmann-like lunar transfers. Both Artemis and GRAIL plan to implement low-energy lunar transfers in the next few years. This paper explores the characteristics and potential applications of many different families of low-energy ballistic lunar transfers. The transfers presented here begin from a wide variety of different orbits at the Earth and follow several different distinct pathways to the Moon. This paper characterizes these pathways to identify desirable low-energy lunar transfers for future lunar missions.
Three-Body Halo Orbits↗
Seasonal Variations of the James Webb Space Telescope Orbital Dynamics
LV separation state is fixed ECEF, so inertial states vary with hourly, daily, monthly, and yearly frequencies The net effect of all frequencies leads to significant variations in orbit geometry Injection states can be matched with invariant manifolds of periodic orbits in the CR3BP to explain observed final orbit.
Three Body Problem↗
Vacancy Relaxation in Cubic Crystals
The configuration of the atoms surrounding a vacancy in four face-centered cubic and three body-centered cubic metals has been computed, using a pairwise, central-force model in which the energy of interaction between two atoms was taken to have the form of a Morse function. Only radial relaxations were considered. The first and second nearest-neighbor relaxations for the face-centered systems were found to be: Pb (1.42,−0.43), Ni (2.14,−0.39), Cu(2.24,−0.40) and Ca (2.73,−0.41, expressed in percentages of normal distances. For the body-centered systems the relaxations out to the fourth nearest neighbors to the vacancy were: Fe (6.07,−2.12, −0.25, −), Ba (7.85, −2.70, 0.70, −0.33) and Na (10.80, −3.14, 3.43, −0.20). The positive signs indicate relaxation toward the vacancy and the negative signs indicate relaxation away from the vacancy. The energies of relaxation (eV) are: Pb (0.162), Ni (0.626), Cu (0.560), Ca (0.400), Fe (1.410), Ba (0.950) and Na (0.172).
Girifalco, L. A.↗
Space Launch System Booster Separation Aerodynamic Database Development and Uncertainty Quantification
The development of the aerodynamic database for the Space Launch System (SLS) booster separation environment has presented many challenges because of the complex physics of the ow around three independent bodies due to proximity e ects and jet inter- actions from the booster separation motors and the core stage engines. This aerodynamic environment is dicult to simulate in a wind tunnel experiment and also dicult to simu- late with computational uid dynamics. The database is further complicated by the high dimensionality of the independent variable space, which includes the orientation of the core stage, the relative positions and orientations of the solid rocket boosters, and the thrust lev- els of the various engines. Moreover, the clearance between the core stage and the boosters during the separation event is sensitive to the aerodynamic uncertainties of the database. This paper will present the development process for Version 3 of the SLS booster separa- tion aerodynamic database and the statistics-based uncertainty quanti cation process for the database.
Chan, David T.↗
Streak Instabilities on HIFiRE-5 Elliptic Cone
The Hypersonic International Flight Research and Experimentation (HIFiRE) 5 flight experiment by the Air Force Research Laboratories and Australian Defense Science and Technology Organization yielded inflight, hypersonic transition data for a canonical, 3D configuration in the form of an elliptic cone at various combinations of angle-of-attack and yaw. Previous analysis has shown that boundary-layer stability calculations for the as-flown, zero-yaw flight conditions are able to capture the second mode dominated transition along the attachment line as well as the crossflow induced transition in between the attachment line and the minor axis symmetry plane. However, there is still a need to understand the transition in the vicinity of the minor axis plane of symmetry, where the boundary layer thickness exhibits an azimuthally compact bulge due to the collision of the secondary flow approaching from the attachment lines on both sides. This paper reports a computational analysis of the stability of the boundary layer flow along the bulge regions on both the leeward and windward sides of the vehicle surface. At a representative flight condition corresponding to a time instant of t = 514.813 seconds, computations are performed to identify several different unstable modes within the bulge regions, with the eventual goal of developing a linear stability correlation for the transition onset near the minor axis symmetry plane. The most amplified flow instabilities in the pretransitional region correspond to a “stem” mode that is concentrated within a pair of nearly vertical shear layers below the cap of the mushroom shaped bulge in the mean velocity contours. An excellent agreement is found between the predictions of instability amplification based on the plane marching parabolized stability equations (PSE) and the direct numerical solutions (DNS). Given the large number of unstable modes within the bulge region, the observed agreement demonstrates, for first time, that the PSE can provide accurate predictions for the development of flow instabilities in streak-like flow features over three-dimensional bodies. The peak N-factor of approximately 15 at the transition location estimated from the thermocouple measurements along the leeward centerline is close to the transition N-factor for Mack mode transition during the HIFiRE-1 circular cone flight experiment with nearly zero degrees angle of attack.
Meelan Choudhari↗
Development of Physics-Based Transition Models for Unstructured-Mesh CFD Codes Using Deep Learning Models
Predicting transition locations over a vehicle surface is of fundamental importance for many engineering applications. With the transition information, the Reynolds-averaged Navier-Stokes (RANS) computations can turn on the turbulence model at the right locations so that drag, lift and other aerodynamic quantities can be accurately predicted. In contrast to the popularity of RANS-based transition modeling in which transition onset is governed by the turbulence equations, physics-based transition models that account for instability waves within the boundary layer, thus more compliant to flow physics, only gained more attention in recent years. This paper describes the development of a new physics-based transition model based on either the linear stability theory (LST) or parabolized stability equations (PSE). The model is designed to communicate with a structured or unstructured-mesh RANS solver back and forth in order to more accurately compute transition fronts over a three-dimensional body. In the developed model, the Python suite of interface codes in conjunction with the LASTRAC software can be executed autonomously to produce transition onset locations for a given laminar or RANS-computed transitional state. In addition, as a proof of concept, the tool set consists of a deep learning neural network model that has been designed and trained to predict instability wave evolutions inside the boundary layer for various instability wave mechanisms across a selected speed range. A machine-learned intelligent profile interpolation model has also been devised to enable reliable instability-wave spectra predictions with just a few points in the mean flow profiles.
Transition Modeling↗
Hypersonic Boundary-Layer Transition over a Blunt Circular Cone in a Mach 8 Digital Wind Tunnel
To understand the effects of freestream acoustic disturbances on transition reversal over a blunt body, three-dimensional direct numerical simulations (DNS) were conducted to investigate the interaction of a tunnel-like acoustic disturbance field with a Mach 8 laminar boundary layer over a 7 deg half-angle blunt cone with a nose radius of 𝑅 𝑛 = 5.2 mm. The flow conditions and the axisymmetric cone geometry matched those measured in the Sandia Hypersonic Wind Tunnel at Mach 8 (Sandia HWT-8), and the incident freestream acoustic disturbances in the DNS were generated by acoustic radiation from the nozzle-wall turbulent boundary layer in the same tunnel. Consistent with the predictions of the nonmodal instability analysis, the study shows the emergence of a second spectral peak for moderately oblique waves between 150 kHz and 200 kHz in the aft part of the cone. The spectral energy of temperature and streamwise velocity fluctuations is initially concentrated within the entropy layer. These fluctiations are eventually “swallowed” by the boundary layer as the entropy-layer thickness 𝛿 𝑆 becomes similar to the boundary-layer thickness 𝛿h𝑡 at downstream locations. The numerical schlieren contours show the same inclined structures commonly observed in blunt cone experiments, and these structures are found to be three dimensional and advect with a constant speed approximately equal to the mean flow speed near the edge of the boundary layer.
Hypersonic Flow↗
Hypersonic Boundary-Layer Transition over a Blunt Circular Cone in a Mach 8 Digital Wind Tunnel
To understand the effects of freestream acoustic disturbances on transition reversal over a blunt body, three-dimensional direct numerical simulations (DNS) were conducted to investigate the interaction of a tunnel-like acoustic disturbance field with a Mach 8 laminar boundary layer over a 7 deg half-angle blunt cone with a nose radius of 𝑅 𝑛 = 5.2 mm. The flow conditions and the axisymmetric cone geometry matched those measured in the Sandia Hypersonic Wind Tunnel at Mach 8 (Sandia HWT-8), and the incident freestream acoustic disturbances in the DNS were generated by acoustic radiation from the nozzle-wall turbulent boundary layer in the same tunnel. Consistent with the predictions of the nonmodal instability analysis, the study shows the emergence of a second spectral peak for moderately oblique waves between 150 kHz and 200 kHz in the aft part of the cone. The spectral energy of temperature and streamwise velocity fluctuations is initially concentrated within the entropy layer. These fluctiations are eventually “swallowed” by the boundary layer as the entropy-layer thickness 𝛿 𝑆 becomes similar to the boundary-layer thickness 𝛿h𝑡 at downstream locations. The numerical schlieren contours show the same inclined structures commonly observed in blunt cone experiments, and these structures are found to be three dimensional and advect with a constant speed approximately equal to the mean flow speed near the edge of the boundary layer.
Hypersonic Flow↗
The investigation of flow instabilities on a rotating disk with curvature in the radial direction
The major objective is to explore any visible differences of the flow field with wall curvature of the test body, including possible interaction between Taylor-Gortler instabilities present along concave walls and the inflexional instabilities investigated here. An experimental study was conducted with emphasis placed on making visual observations and recording photographically the flow instabilities present under three different rotating bodies: a flat disk, a concave paraboloid, and a convex paraboloid. The data collected for the three test bodies lead to the conclusion that the wall curvature of the concave and convex paraboloids did not alter the observed flow field significantly from that observed on the flat disk.
Intemann, P. A.↗