Search NASA⌕ Search

SEARCH · Search NASA

Results for “Surface integration”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Investigation of Volumetric Sources in Airframe Noise Simulations

Hybrid methods for the prediction of airframe noise involve a simulation of the near field flow that is used as input to an acoustic propagation formula. The acoustic formulations discussed herein are those based on the Ffowcs Williams and Hawkings equation. Some questions have arisen in the published literature in regard to an apparently significant dependence of radiated noise predictions on the location of the integration surface used in the solution of the Ffowcs Williams and Hawkings equation. These differences in radiated noise levels are most pronounced between solid-body surface integrals and off-body, permeable surface integrals. Such differences suggest that either a non-negligible volumetric source is contributing to the total radiation or the input flow simulation is suspect. The focus of the current work is the issue of internal consistency of the flow calculations that are currently used as input to airframe noise predictions. The case study for this research is a computer simulation for a three-element, high-lift wing profile during landing conditions. The noise radiated from this flow is predicted by a two-dimensional, frequency-domain formulation of the Ffowcs Williams and Hawkings equation. Radiated sound from volumetric sources is assessed by comparison of a permeable surface integration with the sum of a solid-body surface integral and a volume integral. The separate noise predictions are found in good agreement.

Casper, Jay H.↗
NASA NTRS1997

An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation. This means that the FW-H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Brentner, Kenneth S.↗
NASA NTRS1982

Preliminary analytical results using surface current integration for predicting effects of surface pillows on RF performance

An overview of the fast integral RF evaluation (FIRE) program is presented. This program uses surface current integration to evaluate RF performance of antenna systems. It requires modeling of surfaces in X, Y, Z coordinates along equally spaced X and Y grids with Z in the focal directon. The far field contribution of each surface point includes the effects of the Z-component of surface current which is not included in the aperture integration technique. Because of this, surface current integration is the most effective and inclusive technique for predicting RF performance on non-ideal reflectors. Results obtained from use of the FIRE program and an aperture integration program to predict RF performance of a LSS antenna concept are presented.

Farrell, C. E.↗
NASA NTRS2017

Identification of Spurious Signals from Permeable Ffowcs Williams and Hawkings Surfaces

Integral forms of the permeable surface formulation of the Ffowcs Williams and Hawkings (FW-H) equation often require an input in the form of a near field Computational Fluid Dynamics (CFD) solution to predict noise in the near or far field from various types of geometries. The FW-H equation involves three source terms; two surface terms (monopole and dipole) and a volume term (quadrupole). Many solutions to the FW-H equation, such as several of Farassat's formulations, neglect the quadrupole term. Neglecting the quadrupole term in permeable surface formulations leads to inaccuracies called spurious signals. This paper explores the concept of spurious signals, explains how they are generated by specifying the acoustic and hydrodynamic surface properties individually, and provides methods to determine their presence, regardless of whether a correction algorithm is employed. A potential approach based on the equivalent sources method (ESM) and the sensitivity of Formulation 1A (Formulation S1A) is also discussed for the removal of spurious signals.

Lopes, Leonard V.↗
NASA NTRS1978

Calculation of unsteady transonic flows using the integral equation method

The basic integral equations for a harmonically oscillating airfoil in a transonic flow with shock waves are derived; the reduced frequency is assumed to be small. The problems associated with shock wave motion are treated using a strained coordinate system. The integral equation is linear and consists of both line integrals and surface integrals over the flow field which are evaluated by quadrature. This leads to a set of linear algebraic equations that can be solved directly. The shock motion is obtained explicitly by enforcing the condition that the flow is continuous except at a shock wave. Results obtained for both lifting and nonlifting oscillatory flows agree satisfactorily with other accurate results.

Nixon, D.↗
NASA NTRS2009

Skill Assessment of a Spectral Ocean-Atmosphere Radiative Model

Ocean phytoplankton, detrital material, and water absorb and scatter light spectrally. The Ocean- Atmosphere Spectral Irradiance Model (OASIM) is intended to provide surface irradiance over the oceans with sufficient spectral resolution to support ocean ecology, biogeochemistry, and heat exchange investigations, and of sufficient duration to support inter-annual and decadal investigations. OASIM total surface irradiance (integrated 200 nm to 4 microns) was compared to in situ data and three publicly available global data products at monthly 1-degree resolution. OASIM spectrally-integrated surface irradiance had root mean square (RMS) difference= 20.1 W/sq m (about 11%), bias=1.6 W/sq m (about 0.8%), regression slope= 1.01 and correlation coefficient= 0.89, when compared to 2322 in situ observations. OASIM had the lowest bias of any of the global data products evaluated (ISCCP-FD, NCEP, and ISLSCP 11), and the best slope (nearest to unity). It had the second best RMS, and the third best correlation coefficient. OASIM total surface irradiance compared well with ISCCP-FD (RMS= 20.7 W/sq m; bias=-11.4 W/sq m, r=0.98) and ISLSCP II (RMS =25.2 W/sq m; bias= -13.8 W/sq m; r=0.97), but less well with NCEP (RMS =43.0 W/sq m ;bias=-22.6 W/sq m; x=0.91). Comparisons of OASIM photosynthetically available radiation (PAR) with PAR derived from SeaWiFS showed low bias (-1.8 mol photons /sq m/d, or about 5%), RMS (4.25 mol photons /sq m/d ' or about 12%), near unity slope (1.03) and high correlation coefficient (0.97). Coupled with previous estimates of clear sky spectral irradiance in OASIM (6.6% RMS at 1 nm resolution), these results suggest that OASIM provides reasonable estimates of surface broadband and spectral irradiance in the oceans, and can support studies on ocean ecosystems, carbon cycling, and heat exchange.

Gregg, Watson, W.↗
NASA NTRS2016

Departure Queue Prediction for Strategic and Tactical Surface Scheduler Integration

A departure metering concept to be demonstrated at Charlotte Douglas International Airport (CLT) will integrate strategic and tactical surface scheduling components to enable the respective collaborative decision making and improved efficiency benefits these two methods of scheduling provide. This study analyzes the effect of tactical scheduling on strategic scheduler predictability. Strategic queue predictions and target gate pushback times to achieve a desired queue length are compared between fast time simulations of CLT surface operations with and without tactical scheduling. The use of variable departure rates as a strategic scheduler input was shown to substantially improve queue predictions over static departure rates. With target queue length calibration, the strategic scheduler can be tuned to produce average delays within one minute of the tactical scheduler. However, root mean square differences between strategic and tactical delays were between 12 and 15 minutes due to the different methods the strategic and tactical schedulers use to predict takeoff times and generate gate pushback clearances. This demonstrates how difficult it is for the strategic scheduler to predict tactical scheduler assigned gate delays on an individual flight basis as the tactical scheduler adjusts departure sequence to accommodate arrival interactions. Strategic/tactical scheduler compatibility may be improved by providing more arrival information to the strategic scheduler and stabilizing tactical scheduler changes to runway sequence in response to arrivals.

departure scheduling↗
NASA NTRS1985

Improving the Accuracy of the Boundary Integral Method Based on the Helmholtz Integral

Several recent papers in the literature have been based on various forms of the Helmholtz integral to compute the radiation fields of vibrating bodies. The surface integral form is given. The symbols of P,R micron, rho,G,R,V, and S micron are acoustic pressure, source coordinate, angular frequency, fluid density, Green function, field coordinate, surface velocity and body surface respectively. A discretized form of the surface integral is also given. Solutions to the surface integral are complicated with the singularity of the Green function at R=R micron and with the uniqueness problem at interior eigen frequencies of the enclosed space. The use of the interior integral circumvents the singularity problem since the field points are chosen in the interior space of the vibrating body where a zero pressure condition exists. The interior integral form is given. The method to improve the accuracy is detailed. Examples of the method is presented for a variety of radiators.

Koopmann, G. H.↗
NASA NTRS2001

A Hybrid Numerical Analysis Method for Structural Health Monitoring

A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.

Forth, Scott C.↗
NASA NTRS2002

Numerical Simulations for Landing Gear Noise Generation and Radiation

Aerodynamic noise from a landing gear in a uniform flow is computed using the Ffowcs Williams -Hawkings (FW-H) equation. The time accurate flow data on the surface is obtained using a finite volume flow solver on an unstructured and. The Ffowcs Williams-Hawkings equation is solved using surface integrals over the landing gear surface and over a permeable surface away from the landing gear. Two geometric configurations are tested in order to assess the impact of two lateral struts on the sound level and directivity in the far-field. Predictions from the Ffowcs Williams-Hawkings code are compared with direct calculations by the flow solver at several observer locations inside the computational domain. The permeable Ffowcs Williams-Hawkings surface predictions match those of the flow solver in the near-field. Far-field noise calculations coincide for both integration surfaces. The increase in drag observed between the two landing gear configurations is reflected in the sound pressure level and directivity mainly in the streamwise direction.

Morris, Philip J.↗
NASA NTRS1995

A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations

A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind matching scheme is employed at material interfaces and the Engquist-Majda non-reflecting boundary condition is implemented at the numerical outer boundaries. The staggered leapfrog scheme and the Runge-Kutta methods are utilized for the time integration. Excellent agreements are found between the numerical and analytical solutions.

Liu, Yen↗
NASA NTRS1990

Determination of the Pressure Drag of Airfoils by Integration of Surface Pressures

A study was conducted of the causes of pressure drag of subsonic airfoils. In a previous paper by the author, the pressure drag is obtained by calculating the total drag from the momentum defect in the boundary layer at the trailing edge and subtracting the friction drag obtained from integration of surface friction along the chord. Herein, the pressure drag is obtained by integrating the streamwise components of surface pressure around the airfoil. Studies were made to verify the accuracy of the integration procedure. The values of pressure drag were much smaller than those obtained by the previous method. This lack of agreement is attributed to the difficulty of calculating boundary layer conditions in the vicinity of the trailing edge and to the extreme sensitivity of the circulation and lift to the trailing edge conditions. The results of these studies are compared with those of previous investigations.

Phillips, William H.↗
NASA NTRS1988

Computational technique for compressible vortex flows using the integral equation solution

The steady full-potential equation is written in the form of Poisson's equation, and the solution for the velocity field is expressed in terms of an integral equation. The integral solution consists of two surface integrals and one volume integral. The solution is obtained through successive iteration cycles. Each cycle of iteration consists of two sub-cycles, an inner cycle for wake relaxation and an out cycle for the strength of the source distribution integrals representing the flow compressibility. The density gradients in the source distribution is computed by using a type-differencing scheme of the Murman-Cole type. The method is applied to delta wings and the numerical examples show that a curved shock is captured on the wing suction side beneath the leading edge vortex sheet. Recently, a modified version of the scheme was applied to rectangular wings. In this modified scheme, the surface integral terms were computed by using a bilinear distribution of vorticity on triangular vortex panels which represent the wing and its wake. The results were compared with the available experimental data and they are in good agreement.

Kandil, Osama A.↗
NASA NTRS1998

Integrated Airport Surface Operations

The current air traffic environment in airport terminal areas experiences substantial delays when weather conditions deteriorate to Instrument Meteorological Conditions (IMC). Research activity at NASA has culminated in the development, flight test and demonstration of a prototype Low Visibility Landing and Surface Operations (LVLASO) system. A NASA led industry team and the FAA developed the system which integrated airport surface surveillance systems, aeronautical data links, DGPS navigation, automation systems, and controller and flight deck displays. The LVLASO system was demonstrated at the Hartsfield-Atlanta International Airport using a Boeing 757-200 aircraft during August, 1997. This report documents the contractors role in this testing particularly in the area of data link and DGPS navigation.

Koczo, S.↗
NASA NTRS2013

A T Matrix Method Based upon Scalar Basis Functions

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

wave functions↗
NASA NTRS1987

Energetics of oscillating lifting surfaces using integral conservation laws

The energetics of oscillating flexible lifting surfaces in two and three dimensions is calculated by the use of integral conservation laws in inviscid incompressible flow for general and harmonic transverse oscillations. Total thrust is calculated from the momentum theorem and energy loss rate due to vortex shedding in the wake from the principle of conservation of mechanical energy. Total power required to maintain the oscillations and hydrodynamic efficiency are also determined. In two dimensions, the results are obtained in closed form. In three dimensions, the distribution of vorticity on the lifting surface is also required as input to the calculations. Thus, unsteady lifting-surface theory must be used as well. The analysis is applicable to oscillating lifting surfaces of arbitrary planform, aspect ratio, and reduced frequency and does not require calculation of the leading-edge thrust.

Ahmadi, Ali R.↗
NASA NTRS1991

Advanced development of the boundary element method for elastic and inelastic thermal stress analysis

The focus of this dissertation is on advanced development of the boundary element method for elastic and inelastic thermal stress analysis. New formulations for the treatment of body forces and nonlinear effects are derived. These formulations, which are based on particular integral theory, eliminate the need for volume integrals or extra surface integrals to account for these effects. The formulations are presented for axisymmetric, two and three dimensional analysis. Also in this dissertation, two dimensional and axisymmetric formulations for elastic and inelastic, inhomogeneous stress analysis are introduced. The derivatives account for inhomogeneities due to spatially dependent material parameters, and thermally induced inhomogeneities. The nonlinear formulation of the present work are based on an incremental initial stress approach. Two inelastic solutions algorithms are implemented: an iterative; and a variable stiffness type approach. The Von Mises yield criterion with variable hardening and the associated flow rules are adopted in these algorithms. All formulations are implemented in a general purpose, multi-region computer code with the capability of local definition of boundary conditions. Quadratic, isoparametric shape functions are used to model the geometry and field variables of the boundary (and domain) of the problem. The multi-region implementation permits a body to be modeled in substructured parts, thus dramatically reducing the cost of analysis. Furthermore, it allows a body consisting of regions of different (homogeneous) material to be studied. To test the program, results obtained for simple test cases are checked against their analytic solutions. Thereafter, a range of problems of practical interest are analyzed. In addition to displacement and traction loads, problems with body forces due to self-weight, centrifugal, and thermal loads are considered.

Henry, Donald P., Jr.↗
NASA NTRS2001

The Use of CASES-97 Observations to Assess and Parameterize the Impact of Land-Surface Heterogeneity on Area-Average Surface Heat Fluxes for Large-Scale Coupled Atmosphere-Hydrology Models

To understand the effects of land-surface heterogeneity and the interactions between the land-surface and the planetary boundary layer at different scales, we develop a multiscale data set. This data set, based on the Cooperative Atmosphere-Surface Exchange Study (CASES97) observations, includes atmospheric, surface, and sub-surface observations obtained from a dense observation network covering a large region on the order of 100 km. We use this data set to drive three land-surface models (LSMs) to generate multi-scale (with three resolutions of 1, 5, and 10 kilometers) gridded surface heat flux maps for the CASES area. Upon validating these flux maps with measurements from surface station and aircraft, we utilize them to investigate several approaches for estimating the area-integrated surface heat flux for the CASES97 domain of 71x74 square kilometers, which is crucial for land surface model development/validation and area water and energy budget studies. This research is aimed at understanding the relative contribution of random turbulence versus organized mesoscale circulations to the area-integrated surface flux at the scale of 100 kilometers, and identifying the most important effective parameters for characterizing the subgrid-scale variability for large-scale atmosphere-hydrology models.

Chen, Fei↗