Search NASA⌕ Search

SEARCH · Search NASA

Results for “Differential Geometry”

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.

At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Zero side force volute development

Collector scrolls on high performance centrifugal pumps are currently designed with methods which are based on very approximate flowfield models. Such design practices result in some volute configurations causing excessive side loads even at design flowrates. The purpose of this study was to develop and verify computational design tools which may be used to optimize volute configurations with respect to avoiding excessive loads on the bearings. The new design methodology consisted of a volute grid generation module and a computational fluid dynamics (CFD) module to describe the volute geometry and predict the radial forces for a given flow condition, respectively. Initially, the CFD module was used to predict the impeller and the volute flowfields simultaneously; however, the required computation time was found to be excessive for parametric design studies. A second computational procedure was developed which utilized an analytical impeller flowfield model and an ordinary differential equation to describe the impeller/volute coupling obtained from the literature, Adkins & Brennen (1988). The second procedure resulted in 20 to 30 fold increase in computational speed for an analysis. The volute design analysis was validated by postulating a volute geometry, constructing a volute to this configuration, and measuring the steady radial forces over a range of flow coefficients. Excellent agreement between model predictions and observed pump operation prove the computational impeller/volute pump model to be a valuable design tool. Further applications are recommended to fully establish the benefits of this new methodology.

Anderson, P. G.↗
NASA NTRS1993

On the large eddy simulation of turbulent flows in complex geometry

Application of the method of Large Eddy Simulation (LES) to a turbulent flow consists of three separate steps. First, a filtering operation is performed on the Navier-Stokes equations to remove the small spatial scales. The resulting equations that describe the space time evolution of the 'large eddies' contain the subgrid-scale (sgs) stress tensor that describes the effect of the unresolved small scales on the resolved scales. The second step is the replacement of the sgs stress tensor by some expression involving the large scales - this is the problem of 'subgrid-scale modeling'. The final step is the numerical simulation of the resulting 'closed' equations for the large scale fields on a grid small enough to resolve the smallest of the large eddies, but still much larger than the fine scale structures at the Kolmogorov length. In dividing a turbulent flow field into 'large' and 'small' eddies, one presumes that a cut-off length delta can be sensibly chosen such that all fluctuations on a scale larger than delta are 'large eddies' and the remainder constitute the 'small scale' fluctuations. Typically, delta would be a length scale characterizing the smallest structures of interest in the flow. In an inhomogeneous flow, the 'sensible choice' for delta may vary significantly over the flow domain. For example, in a wall bounded turbulent flow, most statistical averages of interest vary much more rapidly with position near the wall than far away from it. Further, there are dynamically important organized structures near the wall on a scale much smaller than the boundary layer thickness. Therefore, the minimum size of eddies that need to be resolved is smaller near the wall. In general, for the LES of inhomogeneous flows, the width of the filtering kernel delta must be considered to be a function of position. If a filtering operation with a nonuniform filter width is performed on the Navier-Stokes equations, one does not in general get the standard large eddy equations. The complication is caused by the fact that a filtering operation with a nonuniform filter width in general does not commute with the operation of differentiation. This is one of the issues that we have looked at in detail as it is basic to any attempt at applying LES to complex geometry flows. Our principal findings are summarized.

Ghosal, Sandip↗
NASA NTRS1977

Gravitational scattering of zero-rest-mass plane waves

The Feyman-diagram technique is used to calculate the differential cross sections for the scattering of zero-rest-mass plane waves of spin 0, 1, and 2 by linearized Schwarzschild and Kerr geometries in the long-wavelength weak-field limit. It is found that the polarization of right (or left) circularly polarized electromagnetic waves is unaffected by the scattering process (i.e., helicity is conserved) and that the two helicity (polarization) states of the photon are scattered differently by the Kerr geometry. This coupling between the photon helicity and the angular momentum of the scatterer also leads to a partial polarization of unpolarized incident light. For gravitational waves, on the other hand, there is neither helicity conservation nor helicity-dependent scattering; the angular momentum of the scatterer has no polarizing effect on incident unpolarized gravitational waves.

De Logi, W. K.↗
NASA NTRS2015

Improvements to the Tendon-Actuated Lightweight In-Space MANipulator (TALISMAN)

Devices for manipulating and precisely placing payloads are critical for efficient space operations including berthing of spacecraft, in-space assembly, construction and repair. Key to the success of many NASA space activities has been the availability of long-reach crane-like devices such as the Shuttle Remote Manipulation System (SRMS) and the Space Station Remote Manipulation System (SSRMS). These devices have been used for many operations including berthing visiting spacecraft to the International Space Station, deployment of spacecraft, space station assembly, astronaut positioning, payload transfer, and spacecraft inspection prior to atmospheric re-entry. Retiring the Space Transportation System has led to the removal of the SRMS from consideration for in-space missions, thus creating a capability gap. Recognizing this gap, work was initiated at NASA on a new architecture for long-reach space manipulators. Most current devices are constructed by joining revolute joints with carbon composite tubes, with the joints accounting for the majority of the device mass. For example in the case of the SRMS, the entire device mass is 410 kg (904 lbm); the joint structure, motors, gear train, cabling, etc., accounts for the majority of the system mass because the carbon composite tubes mass is 46 kg (101 lbm). An alternate space manipulator concept, the Tendon-Actuated Lightweight In-Space MANipulator (TALISMAN) was created to address deficiencies in the current state-of-the-art in long-reach manipulators. The antagonistic tendon actuated joint architecture allows the motors actuating the joint to be removed from the joint axis, which simplifies the joint design while simultaneously providing mechanical advantage for the motors. The improved mechanical advantage, in turn, reduces the size and power requirements for the motor and gear train. This paper will describe recent architectural improvements to the TALISMAN design that: 1) improve the operational robustness of the system by enabling maneuvers not originally possible by varying the TALISMAN geometry; 2) enable efficient active antagonistic control of a joint while sharing cable between antagonistic tension networks; and 3) uses a unique arrangement of differential capstans to reduce motor torque requirements by an order of magnitude. The paper will also summarize recent efforts to enable autonomous deployment of a TALISMAN including the deployment concept of operations and associated hardware system design. The deployment forces are provided by the same motor systems that are used for articulation, thus reducing the mass associated with the deployment system. The deployment approach is being tested on a TALISMAN prototype which is designed to provide the same operational performance as a shuttle-class manipulator. The prototype has been fabricated and is operational in a new facility at NASA Langley Research Center that has a large area (15.2 m by 21.3 m [50 ft by 70 ft]) air-bearing floor.

Doggett, William R.↗
NASA NTRS1996

Multigrid Methods for EHL Problems

In many bearings and contacts, forces are transmitted through thin continuous fluid films which separate two contacting elements. Objects in contact are normally subjected to friction and wear which can be reduced effectively by using lubricants. If the lubricant film is sufficiently thin to prevent the opposing solids from coming into contact and carries the entire load, then we have hydrodynamic lubrication, where the lubricant film is determined by the motion and geometry of the solids. However, for loaded contacts of low geometrical conformity, such as gears, rolling contact bearings and cams, this is not the case due to high pressures and this is referred to as Elasto-Hydrodynamic Lubrication (EHL) In EHL, elastic deformation of the contacting elements and the increase in fluid viscosity with pressure are very significant and cannot be ignored. Since the deformation results in changing the geometry of the lubricating film, which in turn determines the pressure distribution, an EHL mathematical model must simultaneously satisfy the complex elasticity (integral) and the Reynolds lubrication (differential) equations. The nonlinear and coupled nature of the two equations makes numerical calculations computationally intensive. This is especially true for highly loaded problems found in practice. One novel feature of these problems is that the solution may exhibit sharp pressure spikes in the outlet region. To this date both finite element and finite difference methods have been used to solve EHL problems with perhaps greater emphasis on the use of the finite difference approach. In both cases, a major computational difficulty is ensuring convergence of the nonlinear equations solver to a steady state solution. Two successful methods for achieving this are direct iteration and multigrid methods. Direct iteration methods (e.g Gauss Seidel) have long been used in conjunction with finite difference discretizations on regular meshes. Perhaps one of the best examples of the application of such methods is the recent Effective Influence Method of Dowson and Wang. Multigrid methods have also been used with great success by Venner and Venner and Lubrecht with a good summary being given by Venner. As both these finite difference discretization based approaches appear to provide an efficient way of solving EHL problems, it is important to understand their relative merits. This paper is a first attempt at providing such an understanding in the context of EHL point contact problem, (contact of two spheres), in which the contact zone is a point and an ellipse or circle for unloaded and loaded dry contacts respectively. Since the film thickness and the contact width are generally small compared to the local radius of curvature of the two surfaces, the reduced geometry of the surfaces in the contact area can be accurately approximated to the contact between a paraboloid and a flat surface. The layout of the remainder of this paper is as follows. In section 2 we introduce the form of the equations to be solved. The Effective Influence Newton Method is described in Section 3 while Section 4 describes the Multigrid method to be used. Sections 5 and 6 describe the test problems to be used in the comparison between the two methods and compare the performance of the two methods. Section 7 concludes the paper with an argument of the two methods and suggests some future research directions.

Nurgat, Elyas↗
NASA NTRS2015

Aircraft Measurements of BrO, IO, Glyoxal, NO2, H2O, O2-O2 and Aerosol Extinction Profiles in the Tropics: Comparison with Aircraft-/Ship-Based in Situ and Lidar Measurements

Tropospheric chemistry of halogens and organic carbon over tropical oceans modifies ozone and atmospheric aerosols, yet atmospheric models remain largely untested for lack of vertically resolved measurements of bromine monoxide (BrO), iodine monoxide (IO) and small oxygenated hydrocarbons like glyoxal (CHOCHO) in the tropical troposphere. BrO, IO, glyoxal, nitrogen dioxide (NO2), water vapor (H2O) and O2-O2 collision complexes (O4/ were measured by the University of Colorado Airborne Multi-AXis Differential Optical Absorption Spectroscopy (CU AMAXDOAS) instrument, aerosol extinction by high spectral resolution lidar (HSRL), in situ aerosol size distributions by an ultra high sensitivity aerosol spectrometer (UHSAS) and in situ H2O by vertical-cavity surface-emitting laser (VCSEL) hygrometer. Data are presented from two research flights (RF12, RF17) aboard the National Science Foundation/ National Center for Atmospheric Research Gulfstream V aircraft over the tropical Eastern Pacific Ocean (tEPO) as part of the "Tropical Ocean tRoposphere Exchange of Reactive halogens and Oxygenated hydrocarbons" (TORERO) project (January/February 2012). We assess the accuracy of O4 slant column density (SCD) measurements in the presence and absence of aerosols. Our O4-inferred aerosol extinction profiles at 477 nm agree within 6% with HSRL in the boundary layer and closely resemble the renormalized profile shape of Mie calculations constrained by UHSAS at low (sub-Rayleigh) aerosol extinction in the free troposphere. CU AMAX-DOAS provides a flexible choice of geometry, which we exploit to minimize the SCD in the reference spectrum (SCDREF, maximize signal-to-noise ratio) and to test the robustness of BrO, IO and glyoxal differential SCDs. The RF12 case study was conducted in pristine marine and free tropospheric air. The RF17 case study was conducted above the NOAA RV Ka'imimoana (TORERO cruise, KA-12-01) and provides independent validation data from ship-based in situ cavity-enhanced DOAS and MAX-DOAS. Inside the marine boundary layer (MBL) no BrO was detected (smaller than 0.5 pptv), and 0.2-0.55 pptv IO and 32-36 pptv glyoxal were observed. The near-surface concentrations agree within 30% (IO) and 10% (glyoxal) between ship and air-craft. The BrO concentration strongly increased with altitude to 3.0 pptv at 14.5 km (RF12, 9.1 to 8.6 deg N; 101.2 to 97.4 deg W). At 14.5 km, 5-10 pptv NO2 agree with model predictions and demonstrate good control over separating tropospheric from stratospheric absorbers (NO2 and BrO). Our profile retrievals have 12-20 degrees of freedom (DoF) and up to 500m vertical resolution. The tropospheric BrO vertical column density (VCD) was 1.5 x 10(exp 13) molec cm(exp -2) (RF12) and at least 0.5 x 10(exp 13) molec cm(exp -2) (RF17, 0- 10 km, lower limit). Tropospheric IO VCDs correspond to 2.1 x 10(exp 12) molec cm(exp -2) (RF12) and 2.5 x 10(exp 12) molec cm(exp -2) (RF17) and glyoxal VCDs of 2.6 x 10(exp 14) molec cm(exp -2) (RF12) and 2.7 x 10(exp 14) molec cm(exp -2) (RF17). Surprisingly, essentially all BrO as well as the dominant IO and glyoxal VCD fraction was located above 2 km (IO: 58 plus or minus 5 %, 0.1-0.2 pptv; glyoxal: 52 plus or minus 5 %, 3-20 pptv). To our knowledge there are no previous vertically resolved measurements of BrO and glyoxal from aircraft in the tropical free troposphere. The atmospheric implications are briefly discussed. Future studies are necessary to better understand the sources and impacts of free tropospheric halogens and oxygenated hydrocarbons on tropospheric ozone, aerosols, mercury oxidation and the oxidation capacity of the atmosphere.

Volkamer, R.↗
NASA NTRS1980

Numerical study of baroclinic instability

The effect of a power law gravity field on baroclinic instability is examined with emphasis on the case of inverse fifth power gravity, since this is the power law produced when terrestrial gravity is simulated in spherical geometry by electrostatic means. Growth rates of unstable normal modes were obtained as a function of parameters of the problem by solving a second order differential equation numerically. Results are compared with those from an earlier study where gravity was a constant. The conclusion is that, over the range of parameter space explored here, there is no significant change in the character of theoretical regime diagrams if the vertically averaged gravity is used as a parameter.

Geisler, J. E.↗
NASA NTRS1986

Numerical prediction of cold turbulent flow in combustor configurations with different centerbody flame holders

A numerical study of cold turbulent flow in a combustor containing a centerbody flame holder is presented. The axisymmetric Navier-Stokes equations incorporating a k-epsilon turbulence model were solved in a nonorthogonal curvilinear coordinate system. The finite volume method, applied to a staggered grid system, was used to discretize the differential equations. These finite differenced equations were then solved iteratively utilizing the SIMPLE algorithm described by Patankar (1980). Solutions were obtained for two combustor duct geometries with various centerbody flame holders which included a disk, a cone, and a sphere. The extent of mixing due to these bodies was evaluated. A comparison with previously obtained experimental data yielded moderately good agreement.

Yung, C. N.↗
NASA NTRS1990

Experimental feasibility of investigating acoustic waves in Couette flow with entropy and pressure gradients

The feasibility is discussed for an experimental program for studying the behavior of acoustic wave propagation in the presence of strong gradients of pressure, temperature, and flow. Theory suggests that gradients effects can be experimentally observed as resonant frequency shifts and mode shape changes in a waveguide. A convenient experimental geometry for such experiments is the annular region between two co-rotating cylinders. Radial temperature gradients in a spinning annulus can be generated by differentially heating the two cylinders via electromagnetic induction. Radial pressure gradients can be controlled by varying the cylinder spin rates. Present technology appears adequate to construct an apparatus to allow independent control of temperature and pressure gradients. A complicating feature of a more advanced experiment, involving flow gradients, is the requirement for independently controlled cylinder spin rates. Also, the boundary condition at annulus terminations must be such that flow gradients are minimally disturbed. The design and construction of an advanced apparatus to include flow gradients will require additional technology development.

Parrott, Tony L.↗
NASA NTRS1998

Surface Micromachined Silicon Carbide Accelerometers for Gas Turbine Applications

A finite-element analysis of possible silicon carbide (SIC) folded-beam, lateral-resonating accelerometers is presented. Results include stiffness coefficients, acceleration sensitivities, resonant frequency versus temperature, and proof-mass displacements due to centripetal acceleration of a blade-mounted sensor. The surface micromachined devices, which are similar to the Analog Devices Inc., (Norwood, MA) air-bag crash detector, are etched from 2-pm thick, 3C-SiC films grown at 1600 K using atmospheric pressure chemical vapor deposition (APCVD). The substrate is a 500 gm-thick, (100) silicon wafer. Polysilicon or silicon dioxide is used as a sacrificial layer. The finite element analysis includes temperature-dependent properties, shape change due to volume expansion, and thermal stress caused by differential thermal expansion of the materials. The finite-element results are compared to experimental results for a SiC device of similar, but not identical, geometry. Along with changes in mechanical design, blade-mounted sensors would require on-chip circuitry to cancel displacements due to centripetal acceleration and improve sensitivity and bandwidth. These findings may result in better accelerometer designs for this application.

DeAnna, Russell G.↗
NASA NTRS1976

Pseudopotentials of Estabrook and Wahlquist, the geometry of solitons, and the theory of connections

The prolongation structure of Wahlquist and Estabrook is interpreted as a connection. In this way, some geometric insight might be provided for the description of those nonlinear partial differential equations which admit soliton solutions. A new geometric property - linked to the existence of an SL(2,R) connection - is proved for the solutions of the Korteweg-de Vries equation.

Hermann, R.↗
NASA NTRS2016

Influence of Molecular Simulation Model Accuracy on the Interfacial Properties of an Ionic Liquid: Overview of Recommended Practices

Increasing the energy storage capability of ionic liquid supercapacitors will require better understanding of ion-electrode interactions. We have probed the influence of these interactions on the structure and differential capacitance of of an ionic liquid ([EMIM][BF4]) at an ideal graphite interface as a function of model accuracy. Of note, differential capacitance is determined through newly derived and validated fluctuation formulas. In terms of model accuracy, we test electrostatic techniques, electrode charging techniques, and electrolyte interatomic potentials. For electrostatic summations, we employ high cost, high fidelity techniques as well as less expensive, approximate techniques for summation in slab geometry. For electrode charging, uniform, constant-charge and environmentally responsive, constant-potential conditions are employed. For the ionic liquid, constant charge and atomically polarizable models are employed. We comment on the role of model accuracy on the structure and energetics of the electric double layer as well as on the magnitude and shape of differential capacitance.

simulations↗
NASA NTRS1980

Theoretical regime diagrams for thermally driven flows in a beta-plane channel in the presence of variable gravity

The effect of a power law gravity field on baroclinic instability is examined, with a focus on the case of inverse fifth power gravity, since this is the power law produced when terrestrial gravity is simulated in spherical geometry by a dielectric force. Growth rates are obtained of unstable normal modes as a function of parameters of the problem by solving a second order differential equation numerically. It is concluded that over the range of parameter space explored, there is no significant change in the character of theoretical regime diagrams if the vertically averaged gravity is used as parameter.

Geisler, J. E.↗
NASA NTRS1980

Acoustic transmission matrix of a variable area duct or nozzle carrying a compressible subsonic flow

The differential equations governing the propagation of sound in a variable area duct or nozzle carrying a one dimensional subsonic compressible fluid flow are derived and put in state variable form using acoustic pressure and particle velocity as the state variables. The duct or nozzle is divided into a number of regions. The region size is selected so that in each region the Mach number can be assumed constant and the area variation can be approximated by an exponential area variation. Consequently, the state variable equation in each region has constant coefficients. The transmission matrix for each region is obtained by solving the constant coefficient acoustic state variable differential equation. The transmission matrix for the duct or nozzle is the product of the individual transmission matrices of each region. Solutions are presented for several geometries with and without mean flow.

Miles, J. H.↗
NASA NTRS1980

Acoustic transmission matrix of a variable area duct or nozzle carrying a compressible subsonic flow

The differential equations governing the propagation of sound in a variable area duct or nozzle carrying a one-dimensional subsonic compressible fluid flow are derived and put in state variable form using acoustic pressure and particle velocity as the state variables. The duct or nozzle is divided into a number of regions. The region size is selected so that in each region the Mach number can be assumed constant and the area variation can be approximated by an exponential area variation. Consequently, the state variable equation in each region has constant coefficients. The transmission matrix for each region is obtained by solving the constant coefficient acoustic state variable differential equation. The transmission matrix for the duct or nozzle is the product of the individual transmission matrices of each region. Solutions are presented for several geometries with and without mean flow.

Miles, J. H.↗
NASA NTRS1993

Spatially extensive uniform stress fields on Venus inferred from radial dike swarm geometries: The Aphrodite Terra example

The high resolution and near global coverage of Magellan radar images is facilitating attempts to systematically investigate the stresses that have deformed the venusian crust. Here we continue earlier efforts to utilize approximately 170 large, radially lineated structures interpreted as dike swarms to assess the orientation of the regional maximum horizontal compressive stress (MHCS) which existed in their vicinities during emplacement. Examination of swarms near the equator reveals a link to broad scale regional structures, such as Aphrodite Terra, across distances in excess of 1000 km, suggesting the existence of first order stress fields which affect areas of more than 10(exp 6) sq km in a uniform fashion. Focusing further upon the Aphrodite Terra region, the MHCS field in the surrounding lowlands inferred from radial swarms is oriented approximately normal to the slope of the highland topography. This stress configuration appears, at a simple level, to be incompatible with that expected during either upwelling or downwelling construction of the highlands. In addition, the relatively undeformed geometry of the radial structures within the highlands implies that these dike swarm features formed more recently than their highly deformed surroundings. We conclude that the differential stresses which existed during emplacement of the dike swarms within and adjacent to the Aphrodite Terra highlands are related to the gravitational relaxation of pre-existing topography.

Grosfils, Eric B.↗
NASA NTRS1995

Net-Shape Tailored Fabrics For Complex Composite Structures

Proposed novel looms used to make fabric preforms for complex structural elements, both stiffening elements and skin, from continuous fiber-reinforced composite material. Components of looms include custom reed and differential fabric takeup system. Structural parts made best explained by reference to curved "I" cross-section frame. Technology not limited to these fiber orientations or geometry; fiber angles, frame radius of curvature, frame height, and flange width changed along length of structure. Weaving technology equally applicable to structural skins, such as wing of fuselage skins.

Farley, Gary L.↗
DOE OSTI2025

Numerical assessment of triply periodic minimal surfaces for direct air capture of carbon dioxide

Direct air capture (DAC) systems often consist of packing material wetted by a capture fluid that reacts with CO 2 in the airstream. The efficiency of the contactor is determined by a complex relationship of fluid dynamics, heat and mass transfer, contactor geometry, and chemical properties. The efficiency of the contactor must be balanced with other factors, primarily pressure drop through the system. Triply periodic minimal surfaces (TPMS) are a class of differential surfaces that have been explored in multiple engineering applications and have been shown to exhibit excellent performance when used in heat exchangers. Their tortuous path provides a high surface-to-volume ratio and favorable trade-off between contact area and pressure drop. In this work, a gyroid-type TPMS contactor was evaluated using computational fluid dynamics for a variety of geometric parameters to explore the potential benefit of TPMS shapes for DAC applications. A thin-film model was employed to model the flow and distribution of the capture solvent, allowing efficient simulations of TPMS structures at scale by eliminating the need for a computationally intensive interface capturing method. A liquid-gas mass transfer model was implemented in the commercial software STAR-CCM+ and used to predict the CO 2 capture efficiency and study the trade-off between capture performance and pressure drop through analysis of capture rates, mass transfer coefficients, and other relevant variables. TPMS contactors with a variety of geometric parameters and two capture solvent options were investigated to determine the effect of design choices on the operational performance of DAC systems. In conclusion, results showed that while contactor geometry is the dominant factor in efficiency and pressure drop, the physiochemical properties of the solvent are an important secondary influence on the contactor performance.

CFD↗