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Errors inherent to the graphic analysis of CFD solutions are discussed. Consideration is given to contouring, plotting of vector fields, particle tracing, and the computation of flow functions involving integration or differentiation. Many of the problems addressed are the direct result of knowing the function values only at grid points, not in the interior of the grid cells.
Measurements of the p-mode linewidths over the frequency range v = 1.87-4.93 mHz and degree range 1 = 1-150 are presented. The linewidth is observed to vary with mode frequency and degree. The variation with frequency is consistent with the observations of Libbrecht although the measurements are systematically narrower. The frequency variation has been explained in terms of radiative and convective damping of the modes. The observed variation with degree resolves previous contradictory results and is shown to exceed the 1/S variation that is expected in theoretical grounds. Here S is the travel time of a mode from its lower turning point in the solar interior, to its reflection at the solar surface. The deviations from a 1/S variation suggest that there are two possible damping mechanisms, in addition to radiative and convective damping, that affect the modes.
A Radial Internal Material Handling System (RIMS) has been developed to service a circular floor area in variable gravity. On planetary surfaces, pressurized human habitable volumes will require a means to carry heavy equipment between various locations within the volume of the habitat, regardless of the partial gravity (Earth, moon, Mars, etc). On the NASA Habitat Demonstration Unit (HDU), a vertical cylindrical volume, it was determined that a variety of heavy items would need to be carried back and forth from deployed locations to the General Maintenance Work Station (GMWS) when in need of repair, and other equipment may need to be carried inside for repairs, such as rover parts and other external equipment. The vertical cylindrical volume of the HDU lent itself to a circular overhead track and hoist system that allows lifting of heavy objects from anywhere in the habitat to any other point in the habitat interior. In addition, the system is able to hand off lifted items to other material handling systems through the side hatches, such as through an airlock. This paper describes the RIMS system which is scalable for application in a variety of circular habitat volumes.
On planetary surfaces, pressurized human habitable volumes will require a means to carry equipment around within the volume of the habitat, regardless of the partial gravity (Earth, Moon, Mars, etc.). On the NASA Habitat Demonstration Unit (HDU), a vertical cylindrical volume, it was determined that a variety of heavy items would need to be carried back and forth from deployed locations to the General Maintenance Work Station (GMWS) when in need of repair, and other equipment may need to be carried inside for repairs, such as rover parts and other external equipment. The vertical cylindrical volume of the HDU lent itself to a circular overhead track and hoist system that allows lifting of heavy objects from anywhere in the habitat to any other point in the habitat interior. In addition, the system is able to hand-off lifted items to other material handling systems through the side hatches, such as through an airlock. The overhead system consists of two concentric circle tracks that have a movable beam between them. The beam has a hoist carriage that can move back and forth on the beam. Therefore, the entire system acts like a bridge crane curved around to meet itself in a circle. The novelty of the system is in its configuration, and how it interfaces with the volume of the HDU habitat. Similar to how a bridge crane allows coverage for an entire rectangular volume, the RIMS system covers a circular volume. The RIMS system is the first generation of what may be applied to future planetary surface vertical cylinder habitats on the Moon or on Mars.
The question of how the surface hydrothermal activity (e.g., eruptive plumes and heat flow) is initiated can be addressed within the frame-work of our "Perrier Ocean" model. This model delivers the necessary heat and chemicals to support the heat flow and plumes observed by Cassini in Enceladus' South Polar Region. The model employs closed-loop circulation of water from a sub-surface ocean. The ocean is the main reservoir of heat and chemicals, including dissolved gases. As ocean water moves up toward the surface, pressure is re-duced and gases exsolve forming bubbles. This bub-bly mixture is less dense than the icy crust and the buoyant ocean-water mixture rises toward the surface. Near the surface, heat and chemicals, including some volatiles, are delivered to the chambers in which plumes form and also to shallow reservoirs that keep the surface ice "warm". (Plume operations, per se, are as described by Schmidt et al. and Postberg et al. and are adopted by us.) After transferring heat, the water cools, bubbles contract and dissolve, and the mixture is now relatively dense. It descends through cracks in the crust and returns to the ocean. Once the closed-loop circulation has started it is self-sustaining. Loss of water via the erupting plumes is relatively negligible compared to the amount needed to maintain the heat flow.We note that the activity described herein for the the "Perrier-Ocean" model could, a priori, apply to all small icy bodies that sheltered an interior ocean at some point in their history.
A new numerical method called the Finite Analytical Method for solving partial differential equations is introduced. The basic idea of the finite analytic method is the incorporation of the local analytic solution in obtaining the numerical solution of the problem. The finite analytical method first divides the total region of the problem into small subregions in which local analytic solutions are obtained. Then an algebraic equation is derived from the local analytic solution for each subregion relating an interior nodal value at a point P in the subregion to its neighboring nodal values. The assembly of all the local analytic solutions thus provides the finite-analytic numerical solution of the problem. In this paper the finite analytic method is illustrated in solving steady and unsteady heat transfer problems.
An equation of state for hydrogen which predicts a molecular-metallic phase transition at finite temperatures has become available recently. The effect of this phase transition on the cooling histories of these two giant planets and of substellar brown dwarfs is studied. The phase transition alters the present age of Jupiter and of Saturn by a few percent. Interestingly, the cooling of brown dwarfs is most strongly affected at the time when the interior adiabat crosses the critical point of the phase transition.
A general description of Virtual Reality technology and possible applications was given from publicly available material. A video tape was shown demonstrating the use of multiple large-screen stereoscopic displays, configured in a 10' x 10' x 10' room, to allow a person to evaluate and interact with a vehicle which exists only as mathematical data, and is made only of light. The correct viewpoint of the vehicle is maintained by tracking special glasses worn by the subject. Interior illumination was changed by moving a virtual light around by hand; interior colors are changed by pointing at a color on a color palette, then pointing at the desired surface to change. We concluded by discussing research needed to move this technology forward.
Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.
An elliptic grid generation scheme is described which produces a curvilinear, boundary-fitted grid for highly swept wings with sharp leading edges. The three-dimensional integration domain is segmented in successive crossflow sections wherein the physical coordinates are transformed to computational coordinates by solving an elliptic set of two quasi-linear differential equations. Grid points are clustered in the vicinity of the wing surface, especially in the neighborhood of the leading edges. The formulation of the source terms in the equations governing the transformation contains adjustable parameters which are determined from limiting forms of the elliptic equations along the boundaries. The source terms are assigned to each grid point by interpolation of these parameters into the interior domain. The formulation does not depend on the boundary shape or on the distribution of the grid points along the boundaries. For the first time, the discretized governing equations have been solved using a fast AF1 iteration scheme.
We describe how orbital tunnels could be used to transport payloads through the Earth. If you use a brachistochrone for the tunnel, the body forces in the tunnel become overwhelmingly large for small angular distances traveled. Projectiles move along an orbital tunnel faster than they would along abrachistochrone connecting the same points but the body force components cancel. We describe how parabolic Keplerian orbits outside the object merge onto quasi-Keplerian orbits inside the object. We use models of the interior of the Earth with three values of the polytropic index (n) to calculate interior or bits that travel between surface points. The n¼3 results are also scaled to the Sun. Numerical integrations of the equations describing polytropes were used to generate the initial models. Numerical integration of the equations of motion are then used to calculate the angular distance you can travel along the surface and the traversal time as a function of the parabolic periaps is distance for each model. Trajectories through objects of low central condensation show a focusing effect that decreases as the central condensation increases. Analytic solutions for the trajectories in a homogeneous sphere are derived and compared to the numeric results. The results can be scaled to other planets, stars, or even globular clusters.
Much of the computational effort of the finite element process involves the solution of a system of linear equations. The coefficient matrix of this system, known as the global stiffness matrix, is symmetric, positive definite, and generally sparse. An important technique for reducing the time required to solve this system is substructuring or matrix partitioning. Substructuring is based on the idea of dividing a structure into pieces, each of which can then be analyzed relatively indepenently. As a result of this division, each point in the finite element discretization is either interior to a substructure or on a boundary between substructures. Contributions to the global stiffness matrix from connections between boundary points from the K(bb) matrix are reported. The triangularization of a general K(bb) matrix on a parallel machine is specifically discussed.
A new algorithm for generating solution-adaptive grids (SAG) about airfoil configurations embedded in transonic flow is presented. The present SAG approach uses only the airfoil surface solution to recluster grid points on the airfoil surface, i.e., the reclustering problem is one dimension smaller than the flow-field calculation problem. Special controls automatically built into the elliptic grid generation procedure are then used to obtain grids with suitable interior behavior. This concept of redistributing grid points greatly simplifies the idea of solution-adaptive grids. Numerical results indicate significant improvements in accuracy for SAG grids relative to standard grids using the same number of points.
A nine-element rule is one that makes a classification decision for each pixel based on data from that pixel and its eight immediate neighbors. Three such rules, all fast and simple to use, are defined and tested. All performed substantially better on field interiors than the best one-point rule. Qualitative results indicate that fine detail and contradictory testimony tend to be overlooked by the rules.
A model is presented for the global thermoremanent magnetization of spherical lithospheres which cool in the presence of central dipole fields. Reversals and intensity variations of the field are incorporated in this model, which is applicable to bodies whose interiors have remained above the Curie point throughout their evolution. The model demonstrates that even considering Runcorn's (1975) magnetostatics theorems for spherical shells, a nonzero magnetic permeability and a finite cooling rate in the lithosphere permit the acquisition of a sizable global remanent dipole moment, which would be detectable by external measurements after the magnetizing field has disappeared. Preliminary application of this model to Mercury, Venus, and Mars suggests that only the combination of a nonreversing ancient source field with a surface value near 1 Oe plus a sizable concentration (about 1% by volume) of ferromagnetic material in their crusts could produce remanent planetary dipole fields as large as those measured by spacecraft. On the other hand, if ancient reversing dynamos existed in these planets, it is unlikely that large planetary-scale fields like those observed at Mercury could be due to remanence in their crusts, irrespective of their composition.
The task of removing the boundary layer by suction consists in producing, in place of the ordinary flow with the formation of vortices, another kind of flow in which the vortices are eliminated by drawing small quantities of fluid from certain points on the surface into the interior of the body. The experiments with a sphere, which constitute the subject of this report, were made early in the present year .
The computer code GENIE++ is a continuously evolving grid system containing a multitude of proven geometry/grid techniques. The generation process in GENIE++ is based on an earlier version. The process uses several techniques either separately or in combination to quickly and economically generate sculptured geometry descriptions and grids for arbitrary geometries. The computational mesh is formed by using an appropriate algebraic method. Grid clustering is accomplished with either exponential or hyperbolic tangent routines which allow the user to specify a desired point distribution. Grid smoothing can be accomplished by using an elliptic solver with proper forcing functions. B-spline and Non-Uniform Rational B-splines (NURBS) algorithms are used for surface definition and redistribution. The built in sculptured geometry definition with desired distribution of points, automatic Bezier curve/surface generation for interior boundaries/surfaces, and surface redistribution is based on NURBS. Weighted Lagrance/Hermite transfinite interpolation methods, interactive geometry/grid manipulation modules, and on-line graphical visualization of the generation process are salient features of this system which result in a significant time savings for a given geometry/grid application.
The motivation of this work is the ongoing effort at the Center for Turbulence Research (CTR) to use large eddy simulation (LES) techniques to calculate the noise radiated by jet engines. The focus on engine exhaust noise reduction is motivated by the fact that a significant reduction has been achieved over the last decade on the other main sources of acoustic emissions of jet engines, such as the fan and turbomachinery noise, which gives increased priority to jet noise. To be able to propose methods to reduce the jet noise based on results of numerical simulations, one first has to be able to accurately predict the spatio-temporal distribution of the noise sources in the jet. Though a great deal of understanding of the fundamental turbulence mechanisms in high-speed jets was obtained from direct numerical simulations (DNS) at low Reynolds numbers, LES seems to be the only realistic available tool to obtain the necessary near-field information that is required to estimate the acoustic radiation of the turbulent compressible engine exhaust jets. The quality of jet-noise predictions is determined by the accuracy of the numerical method that has to capture the wide range of pressure fluctuations associated with the turbulence in the jet and with the resulting radiated noise, and by the boundary condition treatment and the quality of the mesh. Higher Reynolds numbers and coarser grids put in turn a higher burden on the robustness and accuracy of the numerical method used in this kind of jet LES simulations. As these calculations are often done in cylindrical coordinates, one of the most important requirements for the numerical method is to provide a flow solution that is not contaminated by numerical artifacts. The coordinate singularity is known to be a source of such artifacts. In the present work we use 6th order Pade schemes in the non-periodic directions to discretize the full compressible flow equations. It turns out that the quality of jet-noise predictions using these schemes is especially sensitive to the type of equation treatment at the singularity axis. The objective of this work is to develop a generally applicable numerical method for treating the singularities present at the polar axis, which is particularly suitable for highly accurate finite-differences schemes (e.g., Pade schemes) on non-staggered grids. The main idea is to reinterpret the regularity conditions developed in the context of pseudo-spectral methods. A set of exact equations at the singularity axis is derived using the appropriate series expansions for the variables in the original set of equations. The present treatment of the equations preserves the same level of accuracy as for the interior scheme. We also want to point out the wider utility of the method, proposed here in the context of compressible flow equations, as its extension for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical coordinates with finite-differences schemes of various level of accuracy is straightforward. The robustness and accuracy of the proposed technique is assessed by comparing results from simulations of laminar forced-jets and turbulent compressible jets using LES with similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r = 0.