Dimensional analysis handbook Arrangement Relationships for Dimensional Analysis /ARDA/
Mathematical procedures for correlating physical data obtained on various sized equipment to establish general physical laws or equations
Mullikin, H. F.↗
SEARCH · Search NASA
Results for “Dimensionality”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Two-dimensional, parabolic boundary value problems as the limiting case of one- dimensional boundary value problems
Explore the source record for details and available documents.
Rothe, E.↗
INPUTB: A thermal/structural data interface program for 2-dimensional and 3-dimensional interpolation
A computer program (INPUTB) for interpolation in both space and time, and based on a linear interpolation scheme using simplex spatial regions is described. The program was developed to provide data interfacing between the output from thermal analyzers and the input to the BOPACE 3-D program. The INPUTB interpolator is of a general nature and could be used for other tasks. The INPUTB program utilizes temperature values which are given at some sequence of time for a list of strategically located thermal nodes. It operates on these values by performing a double interpolation to provide temperature values at another desired sequence of times for a list of structural nodes.
Vos, R. G.↗
Experiments on the stability and transition of two-dimensional and three-dimensional boundary layers with suction
The preliminary experimental development work directed towards the understanding of transition in boundary layers with suction is presented. The basic stability experiment was established and the facility was certified.
Saric, W. S.↗
Interaction of a two-dimensional strip boundary layer with a three-dimensional transonic swept-wing code
A 3D inviscid transonic analysis code was combined with a 2D strip integral boundary layer technique to form an approximate interaction procedure for analyzing the flow over a high aspect ratio wing near cruise conditions. Converged results obtained using the procedure for an aspect ratio 10.3 supercritical wing are discussed. Angle of attack adjustments were made during the iterative procedure in order to compensate for the viscous lift loss. A comparison of the calculations with experimental data is presented.
Newman, P. A.↗
Finite-dimensional compensators for infinite-dimensional systems via Galerkin-type approximation
In this paper existence and construction of stabilizing compensators for linear time-invariant systems defined on Hilbert spaces are discussed. An existence result is established using Galkerin-type approximations in which independent basis elements are used instead of the complete set of eigenvectors. A design procedure based on approximate solutions of the optimal regulator and optimal observer via Galerkin-type approximation is given and the Schumacher approach is used to reduce the dimension of compensators. A detailed discussion for parabolic and hereditary differential systems is included.
Ito, Kazufumi↗
Computation of three-dimensional effects on two dimensional wings
A 2-D numerical investigation was performed to determine the effect of a Gurney flap on a NACA 4412 airfoil. A Gurney flap is a flat plate on the order of 1 to 3 percent of the airfoil chord length, oriented perpendicular to the airfoil chord line and located at the trailing edge of the airfoil. An incompressible Navier Stokes code, INS2D, was used to calculate the flow field about the airfoil. The fully turbulent results were obtained using the Baldwin-Barth one-equation turbulence model. Gurney flap sizes of 0.5, 1, 1.25, 1.5, 2, and 3 percent of the airfoil chord were studied. Computational results were compared with experimental results where possible. The numerical solutions show that the Gurney flap increases airfoil lift coefficient with only a slight increase in drag coefficient. Use of a 1.5 percent chord Gurney flap increases the maximum lift coefficient by approximately 0.3 and decreases the angle of attack for a given lift coefficient by more than 3 degrees. The numerical solutions exhibit detailed flow structures at the trailing edge and provide a possible explanation for the increased aerodynamic performance.
Cummings, Russell M.↗
Comparison of two-dimensional and three-dimensional droplet trajectory calculations in the vicinity of finite wings
Computational predictions of ice accretion on flying aircraft most commonly rely on modeling in 2D. These 2D methods treat an aircraft geometry either as wing-like with infinite span, or as an axisymmetric body. Recently, fully 3D methods have been introduced that model an aircraft's true 3D shape. Because 3D methods are more computationally expensive than 2D methods, 2D methods continue to be widely used. However, a 3D method allows investigation of whether it is valid to continue applying 2D methods to a finite wing. The extent of disagreement between LEWICE, a 2D method, and LEWICE3D, a 3D method, in calculating local collection efficiencies at the leading edge of finite wings is investigated.
Mohler, Stanley R., Jr.↗
Investigation of three-dimensional flow field in a turbine including rotor/stator interaction. II - Three-dimensional flow field at the exit of the nozzle
The nozzle exit flowfield was measured at two axial locations with a miniature five-hole probe. Measurements were taken from hub-to-tip, blade-to-blade at 21 radial locations and at two axial locations downstream of the nozzle trailing edge to resolve the flowfield accurately including the nozzle wake, secondary flow region, horseshoe vortex and losses. All three components of the velocity, stagnation pressure, static pressure, and pitch and yaw angles have been resolved very accurately. The wake data seems to indicate that the decay of the wake is faster than the wake of an isolated nozzle row. The cause of this is attributed to the presence of the rotor downstream. A distinct vortex core has been observed near the tip. The indications are that the horseshoe vortex and the passage vortex have merged to produce a single loss core region. Roughly a third of the blade height passage near the tip and a third of the blade height near the hub is dominated by secondary flow, passage vortex and the horseshoe vortex phenomena. Only the middle third of the nozzle behaves as per design. These and other data are presented, interpreted and synthesized to understand the nozzle flowfield.
Zaccaria, M.↗
Implications of three-dimensional tracer studies for two-dimensional assessments of the impact of supersonic aircraft on stratospheric ozone
A 2D model which uses residual circulation and diffusion and a 3D model which uses winds from a stratospheric data assimilation system are used to estimate transport and dispersion of supersonic aircraft exhaust in the lower stratosphere. The seasonal behavior of the exhaust fields in the two models are is similar, but there is a significant difference in the placement of stratosphere/troposphere exchange in the two models. In the 2D model, exhaust transport to the troposphere occurs mostly at high latitudes, while in the 3D model it occurs at middle latitudes and is clearly associated with synoptic scale events. This may be particularly important to assessment calculations, as the pollutant source is mostly in middle latitudes. The 3D model is also used to examine the transport and dispersion of exhaust in three typical flight corridors: North Atlantic, North Pacific, and tropical. There are no systematic differences that suggest that one corridor is inherently more or less polluting than another.
Douglass, Anne R.↗
The method of space-time conservation element and solution element-applications to one-dimensional and two-dimensional time-marching flow problems
A nontraditional numerical method for solving conservation laws is being developed. The new method is designed from a physicist's perspective, i.e., its development is based more on physics than numerics. Even though it uses only the simplest approximation techniques, a 2D time-marching Euler solver developed recently using the new method is capable of generating nearly perfect solutions for a 2D shock reflection problem used by Helen Yee and others. Moreover, a recent application of this solver to computational aeroacoustics (CAA) problems reveals that: (1) accuracy of its results is comparable to that of a 6th order compact difference scheme even though nominally the current solver is only of 2nd-order accuracy; (2) generally, the non-reflecting boundary condition can be implemented in a simple way without involving characteristic variables; and (3) most importantly, the current solver is capable of handling both continuous and discontinuous flows very well and thus provides a unique numerical tool for solving those flow problems where the interactions between sound waves and shocks are important, such as the noise field around a supersonic over- or under-expansion jet.
Chang, Sin-Chung↗
Three-dimensional structural damage localization system and method using layered two-dimensional array of capacitance sensors
A system and method for detecting damage to a structure is provided. The system includes a voltage source and at least one capacitor formed as a layer within the structure and responsive to the voltage source. The system also includes at least one sensor responsive to the capacitor to sense a voltage of the capacitor. A controller responsive to the sensor determines if damage to the structure has occurred based on the variance of the voltage of the capacitor from a known reference value. A method for sensing damage to a structure involves providing a plurality of capacitors and a controller, and coupling the capacitors to at least one surface of the structure. A voltage of the capacitors is sensed using the controller, and the controller calculates a change in the voltage of the capacitors. The method can include signaling a display system if a change in the voltage occurs.
Curry, Mark A↗
Three-Dimensional Porous Particles Composed of Curved, Two-Dimensional, Nano-Sized Layers for Li-Ion Batteries
Thin Si films coated on porous 3D particles composed of curved 2D graphene sheets have been synthesized utilizing techniques that allow for tunable properties. Since graphene exhibits specific surface area up to 100 times higher than carbon black or graphite, the deposition of the same mass of Si on graphene is much faster in comparison -- a factor which is important for practical applications. In addition, the distance between graphene layers is tunable and variation in the thickness of the deposited Si film is feasible. Both of these characteristics allow for optimization of the energy and power characteristics. Thicker films will allow higher capacity, but slower rate capabilities. Thinner films will allow more rapid charging, or higher power performance. In this innovation, uniform deposition of Si and C layers on high-surface area graphene produced granules with specific surface area (SSA) of 5 sq. m/g.
Yushin, Gleb↗
Mixed three-dimensional and two-dimensional perovskites and methods of making the same
An aspect of the present disclosure is a perovskite that includes A(n−1−nw+w)A′(wn−w)A″2BnX(3n−3zn+3z−4e+1)X′(3zn−3z)X″4e, where each of A, A′, A″ are monovalent cations, B is a divalent cation, each of X, X′, and X″ are monovalent anions, 0<w≤1, 0<z≤1, 0<e≤1, and 1≤n≤100000.
Zhu, Kai↗
Numerical investigations in three-dimensional internal flows
The present study is a preliminary investigation into the behavior of the flow within a 28 degree total geometric turning angle hypothetical Mach 10 inlet as calculated with the full three-dimensional Navier-Stokes equations. Comparison between the two-dimensional and three-dimensional solutions have been made. The overall compression is not significantly different between the two-dimensional and center plane three dimensional solutions. Approximately one-half to two-thirds of the inlet flow at the exit of the inlet behave nominally two-dimensionally. On the other hand, flow field non-uniformities in the three-dimensional solution indicate the potential significance of the sidewall boundary layer flows ingested into the inlet. The tailoring of the geometry at the inlet shoulder and on the cowl obtained in the two-dimensional parametric design study have also proved to be effective at controlling the boundary layer behavior in the three-dimensional code. The three-dimensional inlet solution remained started indicating that the two-dimensional design had a sufficient margin to allow for three-dimensional flow field effects. Although confidence is being gained in the use of SCRAM3D (three-dimensional full Navier-Stokes code) as applied to similar flow fields, the actual effects of the three-dimensional flow fields associated with sidewalls and wind tunnel installations can require verification with ground-based experiments.
Rose, William C.↗
Grassmannian Diffusion Maps--Based Dimension Reduction and Classification for High-Dimensional Data
This work introduces the Grassmannian diffusion maps (GDMaps), a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the Grassmann manifold. Here, the method is designed for applications, such as image recognition and data-based classification of constrained high-dimensional data where each data point itself is a high-dimensional object (i.e., a large matrix) that can be compactly represented in a lower-dimensional subspace. The GDMaps is composed of two stages. The first is a pointwise linear dimensionality reduction wherein each high-dimensional object is mapped onto the Grassmann manifold representing the low-dimensional subspace on which it resides. The second stage is a multipoint nonlinear kernel-based dimension reduction using diffusion maps to identify the subspace structure of the points on the Grassmann manifold. To this end, an appropriate Grassmannian kernel is used to construct the transition matrix of a random walk on a graph connecting points on the Grassmann manifold. Spectral analysis of the transition matrix yields low-dimensional Grassmannian diffusion coordinates embedding the data into a low-dimensional reproducing kernel Hilbert space. Further, a novel data classification/recognition technique is developed based on the construction of an overcomplete dictionary of reduced dimension whose atoms are given by the Grassmannian diffusion coordinates. Three examples are considered. First, a "toy" example shows that the GDMaps can identify an appropriate parametrization of structured points on the unit sphere. The second example demonstrates the ability of the GDMaps to revealing the intrinsic subspace structure of high-dimensional random field data. In the last ex- ample, a face recognition problem is solved considering face images subject to varying illumination conditions, changes in face expressions, and occurrence of occlusions. The technique presented high recognition rates (i.e., 95% in the best case) using a fraction of the data required by conventional methods.
42 ENGINEERING↗
Data Report on Post-Irradiation Dimensional Change of AGC-1 Samples
This report documents the measured post irradiation dimensional change in the AGC-1 samples. The AGC-1 capsule is the first in six planned irradiation capsules comprising the Advanced Graphite Creep (AGC) test series. AGC-1 irradiation began September 5, 2009 in the Advanced Test Reactor (ATR) and was completed on January 8, 2011. The capsule was cooled for 3 months in the ATR Canal, and then shipped to MFC in April 2011 for disassembly and sample extraction. After extraction the samples were shipped to the INL Research Center (IRC) for initial post-irradiation examination (PIE) and storage in the irradiated graphite vault. The AGC-1 capsule design contained “matched pair” samples to ascertain the irradiation-induced dimensional changes and levels of creep experienced in different graphite types. The irradiation-induced dimensional changes and creep levels are determined by comparing the total dimensional change for stressed and unstressed samples of the same type of graphite exposed to the same dose levels and at similar temperatures. Under irradiation creep (i.e. permanent strain due to irradiation, stress, and temperature) the stressed samples should demonstrate more dimensional change than the unstressed samples. This additional dimensional change in the stressed samples is designated as “irradiation-induced creep” in graphite. The data are further presented using the parameters influencing dimensional change in graphite; levels of induced stress, temperature, graphite type, and dose. However, the AGC-1 post-irradiation examination is a significant endeavor and this data report serves to provide irradiation-induced dimensional change data for AGC capsule design refinement as well as a status on the progress of the PIE activities. The dimensional changes of both the samples and graphite body are very important to the design of the future AGC capsules (AGC-3 through AGC-6) and are provided as soon as the data are available in order to determine whether design changes to the next capsule are required. A complete evaluation of the irradiation-induced dimensional change data will be performed for a final AGC-1 PIE report that will include full analysis of pre- and post-irradiation data, with verified AGC-1 irradiation conditions of temperature and dose.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Dynamic realization of emergent high-dimensional optical vortices
The dimensionality of vortical structures has recently been extended beyond two dimensions, providing additional topological complexity and robustness for high-capacity information processing and turbulence control. The generation of high-dimensional vortical structures has mostly been demonstrated in classical systems through the complex interference of fluidic, acoustic, or electromagnetic waves. However, natural materials rarely support three- or higher-dimensional vortical structures and their physical interactions. Here, we experimentally demonstrate a high-dimensional gradient thickness optical cavity (GTOC) in which the optical coupling of planar metal-dielectric multilayers implements topological interactions across multiple dimensions. At non-trivial topological phases, high-dimensional GTOC induces high-dimensional vortical structures in generalized parameter space in three, four dimensions, and beyond. These emergent high-dimensional vortical structures are observed under electro-optic tomography as optical vortex dynamics in two-dimensional real-space, employing the optical thicknesses of dielectric layers as synthetic dimensions. Our findings hold significant promise for emulating high-dimensional physics and developing active topological photonic devices.
36 MATERIALS SCIENCE↗