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At least 127 records · Page 7

Numerical Methods For Chemically Reacting Flows

Issues related to numerical stability, accuracy, and resolution discussed. Technical memorandum presents issues in numerical solution of hyperbolic conservation laws containing "stiff" (relatively large and rapidly changing) source terms. Such equations often used to represent chemically reacting flows. Usually solved by finite-difference numerical methods. Source terms generally necessitate use of small time and/or space steps to obtain sufficient resolution, especially at discontinuities, where incorrect mathematical modeling results in unphysical solutions.

Leveque, R. J.↗

Direct simulation of high-speed mixing layers

A computational study of a nonreacting high-speed mixing layer is performed. A higher order algorithm with sufficient grid points is used to resolve all relevant scales. In all cases, a temporal free-stream disturbance is introduced. The resulting flow is time-sampled to generate a statistical cross section of the flow properties. The studies are conducted at two convective Mach numbers, three free-stream turbulence intensities, three Reynolds numbers, and two types of initial profiles-hyperbolic tangent (tanh) and boundary layer. The boundary-layer profile leads to more realistic predictions of the transition processes. The predicted transition Reynolds number of 0.18 x 10(exp 6) compares well with experimental data. Normalized vortex spacings for the boundary-layer case are about 3.5 and compare favorably with the 1.5 to 2.5 found in experimental measurements. The tanh profile produces spacings of about 10. The growth rate of the layer is shown to be moderately affected by the initial disturbance field, but comparison with experimental data shows moderate agreement. For the boundary-layer case, it is shown that noise at the Strouhal number of 0.007 is selectively amplified and shows little Reynolds number dependence.

Mukunda, H. S.↗

A three-dimensional model of corotating streams in the solar wind. I - Theoretical foundations

The paper is concerned with the development of the theoretical and mathematical background pertinent to the study of steady, corotating solar wind structure in all three spatial dimensions. The dynamical evolution of the plasma in interplanetary space (defined as the region beyond roughly 35 Rs where the flow is supersonic) is approximately described by the nonlinear, single-fluid, polytropic magnetohydrodynamic or hydrodynamic equations. Efficient numerical techniques are outlined for solving this complex system of coupled, hyperbolic partial differential equations. The present formulation is inviscid and nonmagnetic, but the methods used allow for the potential inclusion of both features with only modest modifications. A simple, highly idealized hydrodynamic model stream is examined to illustrate the fundamental processes involved in the three-dimensional dynamics of stream evolution. It is found that spatial variations in the rotational stream interaction mechanism produce small nonradial flows on a global scale that lead to the transport of mass, energy, and momentum away from regions of relative compression and into regions of relative rarefaction. Comparison with simpler models demonstrates the essential nonlinear, multidimensional nature of the interplanetary dynamics.

Pizzo, V.↗

A parallel iterative solution method for systems of nonlinear hyperbolic equations

An iterative algorithm suitable for the solution of a system of nonlinear hyperbolic partial differentiation equations in multiple dimensions is discussed. Current numerical methods for systems of nonlinear PDEs have limited parallelism due to strong coupling between the equations. This method decouples the PDEs by linearizing the convention coefficient for a space-time domain. This provides large grain parallelism. The linearization also allows the treatment of some terms in the equations as source terms, providing more freedom to choose from a wider variety of numerical methods. Smaller grain parallelism may be exploited within the solves for each equation. Thus, the method has potential for parallelism at several levels.

Scroggs, Jeffrey S.↗

Generation of three-dimensional body-fitted coordinates using hyperbolic partial differential equations

An efficient numerical mesh generation scheme capable of creating orthogonal or nearly orthogonal grids about moderately complex three dimensional configurations is described. The mesh is obtained by marching outward from a user specified grid on the body surface. Using spherical grid topology, grids have been generated about full span rectangular wings and a simplified space shuttle orbiter.

Steger, J. L.↗

Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

Cai, Xiao-Chuan↗

Follow-on Research Activities for the Rensselaer Isothermal Dendritic Growth Experiment (RIDGE)

The RIDGE effort continues the aegis of the earlier, NASA-sponsored, Isothermal Dendritic Growth Experiment (IDGE) series of experiments through the continued analysis of microgravity data acquired during these earlier space flights. The preliminary observations presented here demonstrate that there are significant differences between SCN and the more anisotropic PVA dendrites. The side branch structure becomes amplified only further behind the tip, and the interface shape is generally wider (i.e. more hyperbolic than parabolic) in PVA than in SCN. These characteristics are seen to affect the process of heat transport. Additionally, the dendrites grown during the fourth United States Microgravity Payload (USMP-4) exhibit time-dependent growth characteristics and may not always have reached steady-state growth during the experiment.

LaCombe, J. C.↗

Interplanetary trajectory optimization

A procedure for minimizing total impulsive Delta-V for constrained multiple-flyby trajectories, which was originally developed for application to satellite tours, has been modified for application to interplanetary trajectories. The modification includes adding to the cost function the Delta-V required to escape from a parking orbit about the launch planet and the Delta-V required for insertion into orbit about the arrival planet. The hyperbolic excess velocity vector with respect to the launch planet and the launch date have been added to the set of independent variables for the optimization. Each trajectory originates at departure from the parking orbit rather than at a fixed position in space, as is the case for the satellite tour application. The multi-conic trajectory propagation techniques and the Newton optimization algorithm of the original method have been retained. Examples of the application of this new method are given for several types of Galileo interplanetary trajectory options, including Mars powered flyby, broken plane, VEGA, and Delta VEGA trajectories.

Damario, L. A.↗

Some insights into the stability of difference approximations for hyperbolic initial-boundary-value problems

This paper states a conjecture which relates Lax-Richmyer stability to the algebraic test of the stability theory of Gustafsson, Kreiss, and Sundstrom (1972), developed for difference approximations to initial boundary value problems where the matrix size J increases linearly with n as n goes to infinity. This corresponds to mesh refinement in both space and time for t = n x delta t = constant.

Warming, Robert F.↗

Stable boundary approximations for a class of implicit schemes for the one-dimensional inviscid equations of gas dynamics

The applicability to practical calculations of recent theoretical developments in the stability analysis of difference approximations for initial-boundary-value problems of the hyperbolic type. For the numerical experiments, select the one-dimensional inviscid gas-dynamic equations in conservation-law form is selected. A class of implicit schemes based on linear multistep methods for ordinary differential equations is chosen and the use of space or space-time extrapolations as implicit or explicit boundary schemes is emphasized. Some numerical examples with various inflow-outflow conditions highlight the commonly discussed issues: explicit versus implicit boundary schemes, unconditionally stable schemes, and underspecification or overspecification of boundary conditions.

Yee, H. C.↗

On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws

A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the hyperbolicity of the Euler equation system and the first principle of plane (simple) wave propagation. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in ID, 2D and 3D space are illustrated to demonstrate its robustness in practical computations.

Loh, Ching Y.↗

Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations

New numerical algorithms are devised (PSC algorithms) for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand-sides, by using techniques from the hyperbolic conservation laws. Non-oscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be used also for more general Hamilton-Jacobi-type problems. The algorithms are demonstrated by computing the solution to a variety of surface motion problems.

Osher, Stanley↗

Efficient general method for numerically modeling laser pulse propagation, overlap, and lifetime effects in amplifiers

An efficient numerical time-dependent general method is developed to address incoherent pulse overlap and lifetime effects in laser amplifiers. The alternating propagation-population laser energetics method (APPLE) has been validated against a semi-discrete coupled rate equation numerical method (SDRE) and analytic formalisms in bounding cases. APPLE is based on decoupled rates applied to a time-dependent framework where both space-time-dependent populations and pulse energetics are consistently updated in each time step. A significant advantage of APPLE lies in its conceptual simplicity, ease of implementation, and relatively small computational cost. SDRE tracks the populations through coupled rates and uses the method of lines to discretize the hyperbolic partial differential transport equations allowing for use of ordinary differential equation solvers. With reasonably sized mesh, we report both energetic and power pulse shape relative differences on the order of one percent between the models over a large range of initial conditions.

47 OTHER INSTRUMENTATION↗

Higher-order flux difference splitting schemes for the Euler equations using upstream interpolations

A class of explicit two time-level, 2p + 1 space-point, (2p 1)-th order, upwind-biased flux difference splitting schemes are proposed for the numerical advection based on Lagrange's interpolation, and the method is an accord with the physical domain of dependence. A normalized Jacobian coefficient matrix is introduced to convert the schemes to hyperbolic systems of conservation laws, and approaches to make the higher-order schemes total variation stable are discussed. Accuracy and stability of the present schemes are examined, and implicit total variation diminishing schemes are developed for steady-state calculations.Application to gasdynamic problems for both steady and unsteady flows covering a wide range of Mach numbers is considered, and results for a blast wave passing a cylinder, and head-on collision of two blast waves over a circular arc, are presented. The flow patterns were found to be symmetric, and good resolution of flow structures was obtained.

Yang, J. Y.↗

The Origins Space Telescope Integration and Testing

This paper describes the plans, flows, key facilities, test beds, pathfinders, simulators and ground support equipment that could be used to fully integrate, functionally test and qualify the Origins Space Telescope (Origins). The Origins Observatory consists of the Spacecraft Bus Module (SBM) and the Cryogenic Payload Module (CPM), which comprises the telescope and three science instruments. The telescope is a Three Mirror Anastigmat (TMA) and is composed of four mirrors: three with optical power (the elliptical primary, hyperbolic secondary, and elliptical tertiary mirrors) and a flat field-steering mirror (FSM). The three science instruments spanning the wavelength range 2.8 to 588 μm provide the powerful new spectroscopic and imaging capabilities required to achieve the scientific objectives. The Origins Survey Spectrometer (OSS) uses six gratings in parallel to take multi-beam spectra simultaneously across the 25 to 588 μm window through long slits enabling deep 3D extra-galactic surveys. The Far-IR Imager/Polarimeter (FIP) provides imaging and polarimetric measurement capabilities at 50 and 250 μm. Its fast mapping enables rapid follow-up of transient or variable sources and efficient monitoring campaigns. The Mid-Infrared Spectrometer (MISC-T) provides spectroscopy simultaneously over 2.8 to 20 μm with exquisite stability and precision (<5 ppm between 2.8 to 10 μm, <20 ppm between 11 to 20 μm). All the instruments are delivered for Integration and Test fully qualified and calibrated. The Integration and Test program implemented at each level of assembly is discussed as well as the separation of thermal vacuum testing between the hot and cold zones of the Observatory. Portions of this manuscript appear in the Origins Study Final Report.

Origins↗

B-plane Evolution Under Highly Non-Keplerian Dynamics

Juno is the second of a series of New Frontiers missions and was launched in 2011. The spacecraft was set en route to Jupiter, and its Jupiter Orbit Insertion occurred on 2016-07-04 after a five-year cruise in deep space. The mission phase just prior to this large maneuver is called approach. As navigation team, we were responsible for precise orbit determination of the Juno spacecraft to ensure a successful orbit insertion. To evaluate the navigation performance we employed the B-plane mapping, where the incoming hyperbolic velocity defines the plane perpendicular to it, and the time to go to hit the plane will directly map into the uncertainties of the target point. The B-plane is a convenient tool when assessing the navigation performance as it is not affected by non-linearities due to the gravitational pull of the targeted body. However, as the Jupiter Orbit Insertion approached we started to realize that the B-plane mapping uncertainties were significantly larger than expected. We found that the B-plane mapping time had tremendous influence on the covariance inflation in the B-plane. Because of the close approach distance during the Jupiter Orbit Insertion and the strong interaction with J2 spherical harmonic coefficient, the Juno dynamics were too far from a Keplerian one assumed for the B-plane mapping. We first discuss the analytical approach of the B-plane mapping uncertainty and perform a numerical analysis to isolate the components of the Juno dynamics that cause the B-plane covariance inflation.

Bordi, John↗

Technology and the Hubble Space Telescope

The components of the Hubble Space Telescope which is a 13.1 m long, 4.27 m in diameter, and weighs 11,000 kg are described. The telescope will be placed in a 600-km circular orbit of 28.5 deg inclination and it has an expected service life of 15 years. The optical telescope assembly contains the hyperbolic Ritchey-Chretin type primary and secondary mirrors and the optical control system. The telescope is to have a field of view of 28 arcmin in diameter. The use of the fine guidance sensors for pointing stability is examined. The optical and scientific system of the telescope are contained in the support system module. A wide-field/planetary camera, ESA-furnished faint object camera, the high-speed photometer, faint-object spectrograph, high resolution spectrograph, and ESA-furnished solar arrays are located on the telescope. The maintenance and refurbishment of the telescope are discussed. The precise lambda/20 optics, stringent cleanliness, and stable pointing of the telescope produce good image quality for astronomical and solar system science studies.

Mitchell, R. E.↗

Aerocapture: An Enabling Technology for Flagship-Class Uranus Orbiter and Probe Mission

Introduction: The current decadal survey published by the National Academies of Sciences has informed National Aeronautics and Space Administration (NASA) to prioritize the study of the Ice Giants, especially Uranus. To gather the required data that addresses the science questions raised in this survey, a mission to Uranus with an orbiter and atmospheric probe must be designed. The Uranus Orbiter and Probe (UOP) study, which the survey identified as the flagship mission of this decade, proposes a 2031 launch to take advantage of a Jupiter fly-by and utilizes a fully propulsive orbit insertion design with an Earth-to-Uranus transit times ranging from 13 to 15 years. This fully propulsive orbit insertion at Uranus will be very fuel expensive (wet mass percentages of around 60-70\%) thereby leaving less mass for the scientific payload and additional planetary probes. In addition, scientists are more interested in visiting Uranus before 2049, when the Spring Equinox will occur, as it allows studying Uranus seasons not seen during Voyager 2's flyby in 1987. A NASA Flagship-Class mission would require at least 10 years of lead time prior to launch thereby making the 2031 launch to take advantage of the Jupiter fly-by extremely challenging. The consequence of missing the Jupiter fly-by and launching in the late 2030s is the challenge of a fully-propulsive mission like UOP to have a feasible alternative interplanetary trajectory that reaches Uranus before 2050. As an alternative, to address the shortcomings of the fully propulsive mission, one can design a mission to Uranus using aerocapture. What is aerocapture: Aerocapture is an atmospheric maneuver that uses aerodynamic forces generated by flight within a planetary atmosphere to decelerate and achieve orbit insertion. Using aerocapture allows one to provide the change in velocity (Delta V) needed to slow down from the approach hyperbolic trajectory to achieve the desired captured orbit around the target planet using aerodynamic forces of the vehicle (lift and drag). Using aerodynamic forces instead of fully-propulsive maneuvers results in significant savings in the fuel. Furthermore, aerocapture can also allow one to consider interplanetary trajectories with higher approach hyperbolic velocities, thus reducing the mission transit times. Aerocapture as an enabling technology: To use aerocapture as an enabling technology for the Uranus exploration mission, one would require an integrated system-level design, including a Thermal Protection System (TPS), hardware needed for aerodynamic modulation, and autonomous Guidance, Navigation, and Control (GNC) systems. Aerocapture has yet to be demonstrated, despite considering it for several past missions. Recent advancements in TPS and GNC capabilities show the potential for using rigid, heritage entry vehicle configurations already flown at other planetary bodies for Uranus aerocapture. Aerocapture can be a robust technology that can deliver spacecraft to Uranus science orbits while substantially increasing on-orbit payload mass (more than 40\%) that can enable robust atmospheric entry probes. Additionally, the aerocapture maneuver would reduce the interplanetary transit time by 2–5 years (15-30\%) relative to fully-propulsive orbit insertion. Recent work has shown that one can conduct a flagship-class mission in a shorter period than fully-propulsive missions if using aerocapture. What does aerocapture bring in for a Uranus Mission: Using aerocapture for a Uranus orbiter and atmospheric probe mission can provide one with considerable propellant savings. Spacecraft in interplanetary trajectories to Uranus typically need an Delta V in orders of kilometers per second to insert into science orbit. One would require thousands of kilograms of fuel to achieve such a Delta V using a traditional fully propulsive maneuver, leaving less mass for payload during the mission launch. Aerocapture can reduce the propulsion needs by dissipating energy in the sizable atmosphere of Uranus without a significant mass increase due to the need for an aeroshell. One can use the mass savings achieved using the aerocapture to reduce the launch vehicle requirements. In addition, one can also have additional science instruments on the orbiter or create a robust instrumentation suite on an atmospheric probe that can significantly increase the science outcome of the Uranus exploration mission. Furthermore, since aerocapture performance is relatively insensitive to increases in hyperbolic excess velocity, one can design the interplanetary trajectory to arrive at Uranus faster, reducing the interplanetary transit time and operations cost. All these savings, achieved using aerocapture, could help fit a larger class mission, such as the Uranus mission within a smaller capital, e.g., a Flagship-class orbiter mission in a New Frontiers class capital. Summary: This talk will provide an overview of how aerocapture can enable the Uranus exploration mission. Specifically, this talk will discuss the latest advancements made in the Uranus aerocapture study, such as investigating interplanetary trajectories with higher hyperbolic approach velocities and their implications on the aero heating and the TPS design, incorporating FNPAG (an advanced numerical-predictor guidance) and comparison of multiple navigation approaches. In addition, this talk will focus on mechanical design that can house more than one atmospheric probe and the six degrees of freedom simulation of aerocapture at Uranus. Findings from a recent NASA Space Technology Mission Directorate (STMD)-funded activity studying the aerocapture as an enabling technology for a Uranus orbiter will be presented. Using the science payload recommended by the Decadal Survey for Uranus exploration, this work shows many improvements over the baseline fully-propulsive mission. These improvements include a shorter cruise phase, flexibility in launch opportunities late into the 2030s while reaching Uranus before the 2050 equinox for the desired science opportunities, and lower propellant mass needs. This talk will highlight how aerocapture can be utilized for Uranus science orbit insertion using a lower-risk, heritage entry vehicle configuration used extensively as a Mars entry, descent, and landing vehicle. Furthermore, this talk will explore how the demonstration of aerocapture at Earth can benefit the aerocapture-enabled Uranus mission.

Aerocapture↗