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NASA NTRS1993

Thermocapillary migration of a small chain of bubbles

The quasistatic thermocapillary migration of a chain of two or three spherical bubbles in an unbounded fluid possessing a uniform temperature gradient is investigated in the limit of vanishing Reynolds and Peclet numbers. The line of bubble centers is permitted to be either parallel or perpendicular to the direction of the undisturbed temperature gradient. The governing equations are solved by a truncated-series, boundary-collocation technique. Results are presented which demonstrate the impact of the presence of other bubbles on a test bubble. In the three-bubble case, a simple pairwise-additive approximation is constructed from the reflections solution, and found to perform well except when the bubbles are close to each other. Also, features of the flow topology in the fluid are explored. Separated reverse flow wakes are found in the axisymmetric problem, and other interesting structures are noted for the case in which the line of centers is perpendicular to the applied temperature gradient. The observed flow structure is shown to be the result of superposition of simpler basic flows.

Wei, Huailiang↗

NASA NTRS2017

SpaRibs Geometry Parameterization for Wings with Multiple Sections using Single Design

The SpaRibs topology of an aircraft wing has a significant effect on its structural behavior and stability as well as the flutter performance. The development of additive manufacturing techniques like Electron Beam Free Form Fabrication (EBF3) has made it feasible to manufacture aircraft wings with curvilinear spars, ribs (SpaRibs) and stiffeners. In this article a new global-local optimization framework for wing with multiple sections using curvilinear SpaRibs is described. A single design space is used to parameterize the SpaRibs geometry. This method has been implemented using MSC-PATRAN to create a broad range of SpaRibs topologies using limited number of parameters. It ensures C0 and C1 continuities in SpaRibs geometry at the junction of two wing sections with airfoil thickness gradient discontinuity as well as mesh continuity between all structural components. This method is advantageous in complex multi-disciplinary optimization due to its potential to reduce the number of design variables. For the global-local optimization the local panels are generated by an algorithm which is totally based on a set algebra on the connectivity matrix data. The great advantage of this method is that it is completely independent of the coordinates of the nodes of the finite element model. It is also independent of the order in which the elements are distributed in the FEM. The code is verified by optimizing of the CRM Baseline model at trim condition at Mach number equal to 0.85 for five different angle of attack (-2deg, 0deg,2deg,4deg and 6deg). The final weight of the wing is 19,090.61 lb. This value is comparable to that obtained by Qiang et al. 6 (19,269 lb).

wing sections↗

NASA NTRS1990

A study of the topology of dissipating motions in direct numerical simulations of time-developing compressible and incompressible mixing layers

A preliminary investigation of the geometry of flow patterns in numerically simulated compressible and incompressible mixing layers was carried out using 3-D critical point methodology. Motions characterized by high rates of kinetic energy dissipation and/or high enstrophy were of particular interest. In the approach the partial derivatives of the velocity field are determined at every point in the flow. These are used to construct the invariants of the velocity gradient tensor and the rate-of-strain tensor (P, Q, R, and P(sub s), Q(sub s), R(sub s) respectively). For incompressible flow the first invariant is zero. For the conditions of the compressible simulation, the first invariant is found to be everywhere small, relative to the second and third invariants, and so in both cases the local topology at a point is mainly determined by the second and third invariants. The data at every grid point is used to construct scatter plots of Q versus R and Q(sub s) versus R(sub s). Most points map to a cluster near the origin in Q-R space. However, fine scale motions, that is motions which are characterized by velocity derivatives which scale with the square root of R(sub delta), tend to map to regions which lie far from the origin. Definite trends are observed for motions characterized by high enstrophy and/or high dissipation. The observed trends suggest that, for these motions, the second and third invariants of the velocity gradient and rate-of-strain tensors are strongly correlated. The second and third invariants of the rate-of-strain tensor are related by K(-Q(sub s))(exp 3/2), which is consistent with the above scaling of velocity derivatives. The quantity K appears to depend on Reynolds number with an upper limit K = 2(the square root of 3)/9 corresponding to locally axisymmetric flow. For both the compressible and incompressible mixing layer, regions corresponding to high rates of dissipation are found to be characterized by comparable magnitudes of R(sub ij)R(sub ij) and S(sub ij)S(sub ij). For the incompressible mixing layer, regions characterized by the highest values of enstrophy are found to have relatively low strain rates.

Chen, J. H.↗

NASA NTRS1992

A study of the fine scale motions of incompressible time-developing mixing layers

This work is an extension of a project conducted at the previous CTR summer program and was reported by Chen et al. (1990). In that program, the geometry and topology of the dissipating motions in a variety of shear flows was examined. All data was produced by direct numerical simulations (DNS). The partial derivatives of the velocity field were determined at every grid point in the flow and various invariants and related quantities were computed from the velocity gradient tensor. Motions characterized by high rates of kinetic energy dissipation and high enstrophy were of particular interest. Scatter diagrams of the invariants were mapped out and interesting and unexpected patterns were seen. Each type of shear layer produced its own characteristic scatter plot. In the present project, attention is focused on the incompressible plane mixing layer, and the scatter diagrams are replaced with more useful joint probability density contours. Comparison of the topology of the dissipating motions of flows at different Reynolds numbers are made. Also, plane mixing layers at the same Reynolds number but with different initial conditions are compared.

Soria, J.↗

NASA NTRS2000

Winds From Luminous Late-Type Stars: The Effects of Nonlinear Alfven Waves - 1

We present the results of magnetohydrodynamic (MHD) modeling of winds from luminous late-type stars using a 2.5-dimensional, nonlinear MHD computer code. We assume that the wind is generated within an initially hydrostatic atmosphere and is driven by torsional Alfven waves generated at the stellar surface. Two cases of atmospheric topology are considered: case I has longitudinally uniform density distribution and isotropic radial magnetic field over the stellar surface, and case II has an isotropic, radial magnetic field with a transverse density gradient, which we refer to as an "atmospheric hole." We use the same set of boundary conditions for both models. The calculations are designed to model a cool luminous star, for which we assume an initial hydrostatic pressure scale height of 0.072 Stellar Radius, an Alfven wave speed of 92 km/s at the surface, and a wave period of 76 days, which roughly corresponds with the convective turnover time. For case I the calculations produce a wind with terminal velocity of about 22 km/s and a mass loss rate comparable to the expected value of 10(exp -6) Solar Mass/yr. For case II we predict a two-component wind: a fast (25 km/s) and relatively dense wind outside of the atmospheric hole and a slow (1.5 km/s), rarefied wind inside of the hole.

Airapetian, V. S.↗

NASA NTRS1995

Topological structure of the magnetotail as a function of interplanetary magnetic field direction

Magnetic reconnection between the interplanetary magnetic field (IMF) and the geomagnetic field is thought to play a major role in the transfer of solar wind momentum and energy to the magnetosphere. As the angle between the IMF and the geomagnetic field is changed at the bow of the magnetosphere, the topological record of the location of the reconnection region should be recorded in the magnetosheath and on the magnetopause along the flanks of the tail, because the super fast flow freezes strong magnetic gradients formed in the bow reconnection regions into the plasma downstream. In this report, we present results from a three-dimensional, magnetohydrodynamic (MHD), global numerical simulation code for the location of the separatrix between unconnected IMF magnetosheath field lines and reconnected field lines which penetrate the magnetopause and connect to the polar ionosphere. The angle between the IMF direction and the line where the separatrix crosses the magnetopause is shown to be a sensitive function of the IMF clock angle. We also explain how this behavior can be used to derive an approximate relation for the dependence of the cross-polar voltage on the IMF clock angle. We conclude with a note of caution concerning the importance of physical boundary conditions in magnetoplasma simulations.

Fedder, J. A.↗

NASA NTRS1991

Semiautomatic Design Of Zonal Computational Grids

EZGrid is knowledge-based computer program semiautomatically generating zonal computational grids for use in numerical simulations of two-dimensional flows. Zoning necessary because of limitations imposed by size of available computer memory and by topological complexity of typical flow field. Complexity and amount of required memory reduced by dividing flow field into zones, within each of which computational grid refined only to extent necessary to resolve local high gradients. Developed to speed and systematize zoning.

Vogel, Alison Andrews↗

NASA NTRS1999

A Novel Shape Parameterization Approach

This paper presents a novel parameterization approach for complex shapes suitable for a multidisciplinary design optimization application. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft objects animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in a similar manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminated plate structures) and high-fidelity analysis tools (e.g., nonlinear computational fluid dynamics and detailed finite element modeling). This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, and camber. The results are presented for a multidisciplinary design optimization application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, performance, and a simple propulsion module.

Samareh, Jamshid A.↗

NASA NTRS2000

Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD)

This paper presents a multidisciplinary shape parameterization approach. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft object animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in a similar manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminated plate structures) and high-fidelity (e.g., nonlinear computational fluid dynamics and detailed finite element modeling analysis tools. This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, camber, and free-form surface. Results are presented for a multidisciplinary design optimization application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, and a simple performance module.

Samareh, Jamshid A.↗

NASA NTRS2000

Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD)

This paper presents a multidisciplinary shape parameterization approach. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft object animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in the same manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminate plate structures) and high-fidelity (e.g., nonlinear computational fluid dynamics and detailed finite element modeling) analysis tools. This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, camber, and free-form surface. Results are presented for a multidisciplinary application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, and a simple performance module.

Samareh, Jamshid A.↗

NASA NTRS1987

Cosmic ray-modified stellar winds. I - Solution topologies and singularities

In the present two-fluid hydrodynamical model for stellar wind flow modification due to its interaction with Galactic cosmic rays, these rays are coupled to the stellar wind by either hydromagnetic wave scattering or background flow irregularity propagation. The background flow is modified by the cosmic rays via their pressure gradient. The system of equations used possesses a line of singularities in (r, u, P sub c)-space, or a two-dimensional hypersurface of singularities in (r, u, P sub c, dP sub c/dr)-space, where r, u, and P sub c are respectively the radial distance from the star, the radial wind flow speed, and the cosmic ray pressure. The singular points may be nodes, foci, or saddle points.

Ko, C. M.↗

NASA NTRS2009

Magnetopause Reconnection Impact Parameters from Multiple Spacecraft Magnetic Field Measurements

We present a novel technique that exploits multiple spacecraft data to determine the impact parameters of the most general form of magnetic reconnection at the magnetopause. The method consists of a superposed epoch of multiple spacecraft magnetometer measurements that yields the instantaneous magnetic spatial gradients near a magnetopause reconnection site. The gradients establish the instantaneous positions of the spacecraft relative to the reconnection site. The analysis is well suited to evaluating the spatial scales of singular field line reconnection, which is characterized by a two-dimensional x-type topology adjacent and perpendicular to a reconnecting singular field line. Application of the method to Cluster data known to lie in the vicinity of a northward IMF reconnection site establishes a field topology consistent with singular field line reconnection and a normal magnetic field component of 20 nT. The corresponding current structure consists of a 130 km sheet possibly embedding a thinner. bifurcated sheet.

Wendel, Deirdre E.↗

NASA NTRS1989

Region based route planning - Multi-abstraction route planning based on intermediate level vision processing

Intermediate and high level processing operations are performed on vision data for the organization of images into more meaningful, higher-level topological representations by means of a region-based route planner (RBRP). The RBRP operates in terrain scenarios where some or most of the terrain is occluded, proceeding without a priori maps on the basis of two-dimensional representations and gradient-and-roughness information. Route planning is accomplished by three successive abstractions and yields a detailed point-by-point path by searching only within the boundaries of relatively small regions.

Doshi, Rajkumar S.↗

NASA NTRS2019

A Mixed Integer Efficient Global Optimization Algorithm with Multiple Infill Strategy - Applied to a Wing Topology Optimization Problem

With the advancement in high performance computing and numerical optimization techniques,engineering design optimization problems are becoming more complex, larger scale,higher fidelity, and computationally more demanding, requiring longer run times than ever before. There exists methodologies and techniques that can address some of these challenges but very few can address all, and most are limited in the extent that these concerns can be addressed. With the goal of addressing such challenging engineering problems, we developed anew optimization framework, named AMIEGO, that combines concepts from surrogate-based optimization approaches, gradient-based numerical methods, Partial Least Squares, evolutionary algorithms, and Branch-and-Bound, providing newer capabilities that were not previouslyperceived. However, the original version of this framework, in the process of adaptive samplingto explore and exploit the design space, finds only a single sample point per iteration. The efforthere builds upon this previously developed optimization framework to include multiple infillsampling capability that combines the concept of generalized expected improvement function,unsupervised learning, and multi-objective evolutionary technique. To demonstrate, AMIEGOwith the multiple infill capability (called AMIEGO-MIMOS) solves a series of increasingly difficultengineering design optimization problems. The results reveal the performance of the newapproach is problem dependent. When applied to a ten-bar truss problem, the newly proposedmultiple infill strategy consistently leads to a better design solutions when compared to theexisting CPTV method (implemented with the context of the AMIEGO framework). On theother hand, when applied to a mixed-integer high fidelity wing topology optimization problem- MIMOS, despite showing a steeper convergence at the start, eventually leads to an inferiorsolution as compared to CPTV approach. These results also reveal that a small number ofstarting points, in general, are sufficient to lead to a good overall solution.

Mixed-integer optimization↗

NASA NTRS1992

Effects of g-jitter and cross-diffusion on the onset of convection in doubly diffusive systems

The effects of a modulated gravity field in doubly diffusive layers with and without cross-diffusion are studied. Attention is focused on the determination of linear stability criteria for such systems. Floquet theory is used to establish the stability criteria by a systematic analysis of the topology of the neutral curves from which stability boundaries can be constructed. Convective stability boundaries for gravity-modulated doubly cross-diffusive systems are presented for the cases of dynamically free and rigid boundaries. Two physically different forms of layer stratification are considered: (1) imposed independent gradients of two components and (2) a solute gradient induced by a fixed temperature gradient.

Terrones, Guillermo↗

NASA NTRS1994

Thermocapillary motion of deformable drops

The thermocapillary motion of initially spherical drops/bubbles driven by a constant temperature gradient in an unbounded liquid medium is simulated numerically. Effects of convection of momentum and energy, as well as shape deformations, are addressed. The method used is based on interface tracking on a base cartesian grid, and uses a smeared color or indicator function for the determination of the surface topology. Quad-tree adaptive refinement of the cartesian grid is implemented to enhance the fidelity of the surface tracking. It is shown that convection of energy results in a slowing of the drop, as the isotherms get wrapped around the front of the drop. Shape deformation resulting from inertial effects affect the migration velocity. The physical results obtained are in agreement with the existing literature. Furthermore, remarks are made on the sensitivity of the calculated solutions to the smearing of the fluid properties. Analysis and simulations show that the migration velocity depends very strongly on the smearing of the interfacial force whereas it is rather insensitive to the smearing of other properties, hence the adaptive grid.

Haj-Hariri, Hossein↗

NASA NTRS1992

Sub-domain decomposition methods and computational controls for multibody dynamical systems

This paper presents a concurrent methodology to simulate the dynamics of flexible multibody systems with a large number of degrees of freedom. A general class of open-loop structures is treated and a redundant coordinate formulation is adopted. A range space method is used in which the constraint forces are calculated using a preconditioned conjugate gradient method. By using a preconditioner motivated by the regular ordering of the directed graph of the structures, it is shown that the method is order N in the total number of coordinates of the system. The overall formulation has the advantage that it permits fine parallelization and does not rely on system topology to induce concurrency. It can be efficiently implemented on the present generation of parallel computers with a large number of processors. Validation of the method is presented via numerical simulations of space structures incorporating large number of flexible degrees of freedom.

Menon, R. G.↗

NASA NTRS1996

Refinement Of Hexahedral Cells In Euler Flow Computations

Topologically Independent Grid, Euler Refinement (TIGER) computer program solves Euler equations of three-dimensional, unsteady flow of inviscid, compressible fluid by numerical integration on unstructured hexahedral coordinate grid refined where necessary to resolve shocks and other details. Hexahedral cells subdivided, each into eight smaller cells, as needed to refine computational grid in regions of high flow gradients. Grid Interactive Refinement and Flow-Field Examination (GIRAFFE) computer program written in conjunction with TIGER program to display computed flow-field data and to assist researcher in verifying specified boundary conditions and refining grid.

Melton, John E.↗