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The use of a hybrid computer in the solution of trajectory optimization problems is described. The solution technique utilizes the indirect method and requires iterative computation of the initial condition vector of the co-state variables. Convergence of the iteration is assisted by feedback switching and contour modification. A simulation of the method in an on-line updating scheme is presented.
We have cataloged 160 CMEs detected in the HELIOS 1 and 2 90 deg zodiacal light photometers observed from 1975-1985. The HELIOS 1 and 2 spacecraft orbited from 0.3 to 1.0 AU on 6-month orbits. From the photometer observations of Thomson-scattered light in the inner heliosphere, we have determined CME masses for these events using two methods: (1) by integration over the contours drawn between the three photometers at a given time; and (2) by integration of the mass flow over time past a given photometer. The second method, not readily available using coronagraph observations, is derived from CME speeds measured by using the timing of the peak CME brightness from the 16 deg to 31 deg sets of photometers. The two different HELIOS methods of determining CME mass are consistent with one another for individual CMEs. We find that the CME mass values range from 10(exp 15)g to nearly 10(exp 17)g. We compare the mass distributions of HELIOS-measured CMEs with those from coronagraphs and find that CMEs measured by HELIOS over the same time interval are generally more massive. The solar cycle variation of the total CME mass present in the heliosphere varies by over a factor of approximately 15 from solar minimum to solar maximum. Slightly more massive CMEs carry the bulk of the CME mass during maximum. The total CME mass at solar maximum is found to be near 15% of the total solar wind mass.
The accuracy and order of three bicharacteristic schemes based on the numerical method of characteristics for three-dimensional, steady, isentropic, supersonic flow were compared based on numerical calculations. Comparisons were made for source flows and for flows in contoured axisymmetric nozzles. The first two methods were tetrahedral line networks, differing only in the manner in which the cross derivatives were evaluated. The third method was the pentahedral line network proposed by Butler. All three methods were numerically stable and produced efficient and accurate solutions. A discussion of the relative merits and disadvantages of each method is presented.
This report documents the formulation of a novel level-set method for incompressible two-phase flows in the continuous Galerkin (CG) high order spectral element framework. The overall method hinges on a novel implementation of the spectral vanishing viscosity (SVV) operator for the stabilization of linear/non-linear hyperbolic problems. The multidimensional SVV convolution kernels, which in essence, have a similar effect as a high pass filter applied to the derivatives, are formulated by exploiting the tensor product form, analogous to the construction of the usual stiffness matrix system. The resulting kernels are directionally decoupled and ensure a linear, symmetric positive definite, elliptic matrix operator. The SVV formulation is demonstrated to provide a robust stabilizing mechanism through challenging linear and non-linear hyperbolic problems, including problems pertinent to the level-set formulation. The two-phase framework conceptualized herein is based on the conservative level-set (CLS) method which represents the interface between the fluids by the 0.5 iso-contour of the smoothed Heaviside function. The CLS method is augmented with a preconditioning procedure for interface normals using the signed distance function which precludes the manifestation of spurious oscillations in the vicinty of the interface. Further, the existing mixed explicit-implicit approach for the solution of Navier-Stokes equations in Nek5000, as described in Tomboulides et al, is augmented with a pressure coefficient splitting approach for the Poisson equation, which greatly accelerated the convergence of pressure solver for two-phase systems with large density ratio. The robustness and accuracy of the overall two-phase method is demonstrated through canonical challenging problems involving high density and viscosity ratios, with and without surface tension. The two-phase formulation is wholly implemented in Nek5000 and the SVV stabilization method is implemented in NekRS, which is the essential precursor to the two-phase framework, undergoing active development.
The performance of two axisymmetric nozzles which were designed to produce uniform, parallel flow with nominal Mach numbers of 4 and 8 is examined. A free-piston-driven shock tube was used to supply the nozzle with high-temperature, high-pressure test gas. The inviscid design procedure treated the nozzle expansion in two stages. Close to the nozzle throat, the nozzle wall was specified as conical and the gas flow was treated as a quasi-one-dimensional chemically-reacting flow. At the end of the conical expansion, the gas was assumed to be calorically perfect, and a contoured wall was designed (using method of characteristics) to convert the source flow into a uniform and parallel flow at the end of the nozzle. Performance was assessed by measuring Pitot pressures across the exit plane of the nozzles and, over the range of operating conditions examined, the nozzles produced satisfactory test flows. However, there were flow disturbances in the Mach 8 nozzle flow that persisted for significant times after flow initiation.
The performance of two axisymmetric nozzles which were designed to produce uniform, parallel flow with nominal Mach numbers of 4 and 8 is examined. A free-piston-driven shock tube was used to supply the nozzle with high-temperature, high-pressure test gas. The inviscid design procedure treated the nozzle expansion in two stages. Close to the nozzle throat, the nozzle wall was specified as conical and the gas flow was treated as a quasi-one-dimensional chemically-reacting flow. At the end of the conical expansion, the gas was assumed to be calorically perfect, and a contoured wall was designed (using method of characteristics) to convert the source flow into a uniform and parallel flow at the end of the nozzle. Performance was assessed by measuring Pitot pressures across the exit plane of the nozzles and, over the range of operating conditions examined, the nozzles produced satisfactory test flows. However, there were flow disturbances in the Mach 8 nozzle flow that persisted for significant times after flow initiation.
Current inspection methods for complex shapes and contours exemplified by aircraft engine turbine blades are expensive, time-consuming and labor intensive. The logistics support of new manufacturing paradigms such as integrated product-process development (IPPD) for current and future engine technology development necessitates high speed, automated inspection of forged and cast jet engine blades, combined with a capability of retaining and retrieving metrology data for process improvements upstream (designer-level) and downstream (end-user facilities) at commercial and military installations. The paper presents the opportunities emerging from a feasibility study conducted using 3-D holographic laser radar in blade inspection. Requisite developments in computing technologies for systems integration of blade inspection in production are also discussed.
Gradient vector flow (GVF), an elegant external force for parametric deformable models, can capture object boundaries from both sides. A new geometric deformable model is proposed that combines GVF and the geodesic active contour model. The level set method is used as the numerical method of this model. The model is applied for echocardiographic image segmentation.
When creating training data for machine-learned interatomic potentials (MLIPs), it is common to create initial structures and evolve them using molecular dynamics (MD) to sample a larger configuration space. Here, we benchmark two other modalities of evolving structures, contour exploration (CE) and dimer-method (DM) searches against MD for their ability to produce diverse and robust density functional theory training data sets for MLIPs. We also discuss the generation of initial structures which are either from known structures or from random structures in detail to further formalize the structure-sourcing processes in the future. The polymorph-rich zirconium-oxygen composition space is used as a rigorous benchmark system for comparing the performance of MLIPs trained on structures generated from these structural evolution methods. Using Behler–Parrinello neural networks as our MLIP models, we find that CE and the DM searches are generally superior to MD in terms of spatial descriptor diversity and statistical accuracy.
The surface responses due to impact load on an infinite uniaxial graphite/epoxy plate with and without delamination cracks are investigated both in time and frequency domain by using a hybrid method combining the finite element discretization of the near-field with boundary integral representation of the field outside a contour enclosing completely the crack. This combined method leads to a set of linear unsymmetric complex matrix equations which are solved to obtain the response in the frequency domain by biconjugate gradient method. The time domain response is then obtained by using an FFT. In order to capture the time-domain characteristics accurately, high order finite elements have been used. Also, both the six node singular elements and eight node transition elements are used around the crack tips to model the crack-tip singularity. It is shown that from the numerical results for surface responses both depth and length of this crack can be identified.
Digital imaging techniques are utilized as a measure of surface displacement components in laser speckle metrology. An image scanner which is interfaced to a computer records and stores in memory the laser speckle patterns of an object in a reference and deformed configuration. Subsets of the deformed images are numerically correlated with the references as a measure of surface displacements. Discrete values are determined around a closed contour for plane problems which then become input into a boundary integral equation method in order to calculate surface traction in the contour. Stresses are then calculated within this boundary. The solution procedure is illustrated by a numerical example of a case of uniform tension.
This report covers a comprehensive research study of Androforming, explosive forming, and stretch forming as applied to shaping a parabolic reflector segment for use in a solar furnace. Development efforts were directed toward attaining accurate part contour, and assurance of process reproducibility. The three forming processes mentioned above were investigated by qualified contractors. Three test segments formed by each method along with a detailed analysis were submitted to MSFC. It was concluded that optimum results could be obtained with the stretch forming process. The three test segments of the solar concentrator tha.t were produced by this method, and evaluated optically, revealed a maximum contour deviation of O. 76 degrees.
A new procedure is demonstrated for optimizing hypersonic wind-tunnel-nozzle contours. The procedure couples a CFD computer code to an optimization algorithm, and is applied to both conical and contoured hypersonic nozzles for the purpose of determining an optimal set of parameters to describe the surface geometry. A design-objective function is specified based on the deviation from the desired test-section flow-field conditions. The objective function is minimized by optimizing the parameters used to describe the nozzle contour based on the solution to a nonlinear least-squares problem. The effect of the changes in the nozzle wall parameters are evaluated by computing the nozzle flow using the parabolized Navier-Stokes equations. The advantage of the new procedure is that it directly takes into account the displacement effect of the boundary layer on the wall contour. The new procedure provides a method for optimizing hypersonic nozzles of high Mach numbers which have been designed by classical procedures, but are shown to produce poor flow quality due to the large boundary layers present in the test section. The procedure is demonstrated by finding the optimum design parameters for a Mach 10 conical nozzle and a Mach 6 and a Mach 15 contoured nozzle.
The feasibility of automatically reducing a form of pictorial aerodynamic heating data is discussed. The imagery, depicting the melting history of a thin coat of fusible temperature indicator painted on an aerodynamically heated model, was previously reduced by manual methods. Careful examination of various lighting theories and approaches led to an experimentally verified illumination concept capable of yielding high-quality imagery. Both digital and video image processing techniques were applied to reduction of the data, and it was demonstrated that either method can be used to develop superimposed contours. Mathematical techniques were developed to find the model-to-image and the inverse image-to-model transformation using six conjugate points, and methods were developed using these transformations to determine heating rates on the model surface. A video system was designed which is able to reduce the imagery rapidly, economically and accurately. Costs for this system were estimated. A study plan was outlined whereby the mathematical transformation techniques developed to produce model coordinate heating data could be applied to operational software, and methods were discussed and costs estimated for obtaining the digital information necessary for this software.
An iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical distribution of pressure. The calculations are initialized by using a surface panel method to analyze a baseline wing or wing-fuselage configuration. A first-order expansion to the baseline panel method equations is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter. In every iteration cycle, the matrix is used both to calculate the geometry perturbation and to analyze the perturbed geometry. The distribution of potential on the perturbed geometry is established by simple linear extrapolation from the baseline solution. The extrapolated potential is converted to pressure by Bernoulli's equation. Not only is the accuracy of the approach good for very large perturbations, but the computing cost of each complete iteration cycle is substantially less than one analysis solution by a conventional panel method.
Highly underexpanded free jet boundary contours
In many applications, the data consist of discrete 3-D points at which one or more parameters are given. To display contours, the data are represented by a continuous function which is evaluated at any point as needed for contouring. Contouring results are presented which are applicable both to artitrarily spaced data and to data which lie on a topologically rectangular three dimensional grid. the contours are assumed to be described by 3-D display lists for viewing on a dynamic color graphics device; that is, they will not simply be projected into 2-D and viewed as a static image on a frame buffer. Dynamic viewing of color contours may be essential to the proper interpretation of results. The gridded data lie on a topologically rectangular grid although two or more nodes may be the same point. Parametric tensor product methods may be used to fit the gridded data and to generate the contours. Rectangular elements are convenient but not necessary. For example, there are other methods which are effective for contouring over tetrahedral elements.
Two-neutrino double-beta (2νββ) decay has been used to constrain the neutron-proton part of effective interactions, which in turn is used to compute the nuclear matrix elements for neutrinoless double-beta decay, the observation of which would have important consequences for fundamental physics. We carefully examine 2νββ matrix elements within the proton-neutron quasiparticle random-phase approximation with nuclear energy density functionals. Here we work with functionals that are fit globally to single-beta-decay half-lives and charge-exchange giant-resonance energies, but not to 2νββ half-lives themselves, to evaluate the 2νββ nuclear matrix elements for all important nuclei, including those whose half-lives have not yet been measured. Such a comprehensive evaluation in large model spaces without configuration truncation requires an efficient computational scheme; we employ a double contour integration within the finite amplitude method. The results generally reproduce the nuclear matrix element extracted from half-lives well, without the use of any of those half-lives in the fitting procedure. We present predictions of the matrix elements in a total of 27 nuclei with half-lives that are still unmeasured.