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NASA NTRS2000

Radiative Transfer and Satellite Remote Sensing of Cirrus Clouds Using FIRE-2-IFO Data

Under the support of the NASA grant, we have developed a new geometric-optics model (GOM2) for the calculation of the single-scattering and polarization properties for arbitrarily oriented hexagonal ice crystals. From comparisons with the results computed by the finite difference time domain (FDTD) method, we show that the novel geometric-optics can be applied to the computation of the extinction cross section and single-scattering albedo for ice crystals with size parameters along the minimum dimension as small as approximately 6. We demonstrate that the present model converges to the conventional ray tracing method for large size parameters and produces single-scattering results close to those computed by the FDTD method for size parameters along the minimum dimension smaller than approximately 20. We demonstrate that neither the conventional geometric optics method nor the Lorenz-Mie theory can be used to approximate the scattering, absorption, and polarization features for hexagonal ice crystals with size parameters from approximately 5 to 20. On the satellite remote sensing algorithm development and validation, we have developed a numerical scheme to identify multilayer cirrus cloud systems using AVHRR data. We have applied this scheme to the satellite data collected over the FIRE-2-IFO area during nine overpasses within seven observation dates. Determination of the threshold values used in the detection scheme are based on statistical analyses of these satellite data.

Source record↗
NASA NTRS2000

Radiative Properties of Cirrus Clouds in the Infrared (8-13 microns) Spectral Region

Atmospheric radiation in the infrared (IR) 8-13 microns spectral region contains a wealth of information that is very useful for the retrieval of ice cloud properties from aircraft or space-borne measurements. To provide the scattering and absorption properties of nonspherical ice crystals that are fundamental to the IR retrieval implementation, we use the finite-difference time domain (FDTD) method to solve for the extinction efficiency, single-scattering albedo, and the asymmetry parameter of the phase function for ice crystals smaller than 40 microns. For particles larger than this size, the improved geometric optics method (IGOM) can be employed to calculate the asymmetry parameter with an acceptable accuracy, provided that we properly account for the inhomogeneity of the refracted wave due to strong absorption inside the ice particle. A combination of the results computed from the two methods provides the asymmetry parameter for the entire practical range of particle sizes between 1 micron and 10000 microns over wavelengths ranging from 8 microns to 13 microns. For the extinction and absorption efficiency calculations, several methods including the IGOM, Mie solution for equivalent spheres (MSFES), and the anomalous diffraction theory (ADT) can lead to a substantial discontinuity in comparison with the FDTD solutions for particle sizes on the order of 40 microns. To overcome this difficulty, we have developed a novel approach called the stretched scattering potential method (SSPM). For the IR 8-13 microns spectral region, we show that SSPM is a more accurate approximation than ADT, MSFES, and IGOM. The SSPM solution can be further refined numerically. Through a combination of the FDTD and SSPM, we have computed the extinction and absorption efficiency for hexagonal ice crystals with sizes ranging from 1 to 10000 microns at 12 wavelengths between 8 and 13 microns Calculations of the cirrus bulk scattering and absorption properties are performed for 30 size distributions obtained from various field campaigns for midlatitude and tropical cirrus cloud systems. Parameterization of these bulk scattering properties is carried out by using second-order polynomial functions for the extinction efficiency and the single-scattering albedo and the power law expression for the asymmetry parameter. We note that the volume-normalized extinction coefficient can be separated into two parts: one is inversely proportional to effective size and is independent of wavelength, and the other is the wavelength-dependent effective extinction efficiency. Unlike conventional parameterization efforts, the present parameterization scheme is more accurate because only the latter part of the volume-normalized extinction coefficient is approximated in terms of an analytical expression. After averaging over size distribution, the single-scattering albedo is shown to decrease with an increase in effective size for wavelengths shorter than 10.0 microns whereas the opposite behavior is observed for longer wavelengths. The variation of the asymmetry parameter as a function of effective size is substantial when the effective size is smaller than 50 microns. For effective sizes larger than 100 microns, the asymmetry parameter approaches its asymptotic value. The results derived in this study can be useful to remote sensing applications involving IR window bands under cirrus cloud conditions.

Yang, Ping↗
NASA NTRS2001

Retrieval of Polar Stratospheric Cloud Microphysical Properties from Lidar Measurements: Dependence on Particle Shape Assumptions

A retrieval algorithm has been developed for the microphysical analysis of polar stratospheric cloud (PSC) optical data obtained using lidar instrumentation. The parameterization scheme of the PSC microphysical properties allows for coexistence of up to three different particle types with size-dependent shapes. The finite difference time domain (FDTD) method has been used to calculate optical properties of particles with maximum dimensions equal to or less than 2 mu m and with shapes that can be considered more representative of PSCs on the scale of individual crystals than the commonly assumed spheroids. Specifically. these are irregular and hexagonal crystals. Selection of the optical parameters that are input to the inversion algorithm is based on a potential data set such as that gathered by two of the lidars on board the NASA DC-8 during the Stratospheric Aerosol and Gas Experiment 0 p (SAGE) Ozone Loss Validation experiment (SOLVE) campaign in winter 1999/2000: the Airborne Raman Ozone and Temperature Lidar (AROTEL) and the NASA Langley Differential Absorption Lidar (DIAL). The 0 microphysical retrieval algorithm has been applied to study how particle shape assumptions affect the inversion of lidar data measured in leewave PSCs. The model simulations show that under the assumption of spheroidal particle shapes, PSC surface and volume density are systematically smaller than the FDTD-based values by, respectively, approximately 10-30% and approximately 5-23%.

Reichardt, J.↗
NASA NTRS2004

2004: Finite-Difference Time Domain Solution of Light Scattering by an Infinite Dielectric Column Immersed in an Absorbing Medium

The two-dimensional (2-D) finite-difference time domain (FDTD) method is applied to calculate light scattering and absorption by an arbitrarily shaped infinite column embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition (ABC) is used to truncate the computational domain. The single-scattering properties of the infinite column embedded in the absorbing medium, including scattering phase functions, extinction and absorption efficiencies, are derived using an area integration of the internal field. An exact solution for light scattering and absorption by a circular cylinder in an absorbing medium is used to examine the accuracy of the 2-D UPML FDTD code. With use of a cell size of 1/120 incident wavelength in the FDTD calculations, the errors in the extinction and absorption efficiencies and asymmetry factors from the 2-D UPML FDTD are generally smaller than approx .1%. The errors in the scattering phase functions are typically smaller than approx .4%. Using the 2-D UPML FDTD technique, light scattering and absorption by long noncircular columns embedded in absorbing media can be accurately solved.

Sun, W.↗
NASA NTRS2004

Sampling Versus Filtering in Large-Eddy Simulations

A LES formalism in which the filter operator is replaced by a sampling operator is proposed. The unknown quantities that appear in the LES equations originate only from inadequate resolution (Discretization errors). The resulting viewpoint seems to make a link between finite difference approaches and finite element methods. Sampling operators are shown to commute with nonlinearities and to be purely projective. Moreover, their use allows an unambiguous definition of the LES numerical grid. The price to pay is that sampling never commutes with spatial derivatives and the commutation errors must be modeled. It is shown that models for the discretization errors may be treated using the dynamic procedure. Preliminary results, using the Smagorinsky model, are very encouraging.

Debliquy, O.↗
NASA NTRS2017

Heating and Thermal Control of Brazing Technique to Break Contamination Path for Potential Mars Sample Return

The potential return of Mars sample material is of great interest to the planetary science community, as it would enable extensive analysis of samples with highly sensitive laboratory instruments. It is important to make sure such a mission concept would not bring any living microbes, which may possibly exist on Mars, back to Earth’s environment. In order to ensure the isolation of Mars microbes from Earth’s Atmosphere, a brazing sealing and sterilizing technique was proposed to break the Mars-to-Earth contamination path. Effectively, heating the brazing zone in high vacuum space and controlling the sample temperature for integrity are key challenges to the implementation of this technique. The break-the-chain procedures for container configurations, which are being considered, were simulated by multi-physics finite element models. Different heating methods including induction and resistive/radiation were evaluated. The temperature profiles of Martian samples in a proposed container structure were predicted. The results show that the sealing and sterilizing process can be controlled such that the samples temperature is maintained below the level that may cause damage, and that the brazing technique is a feasible approach to breaking the contamination path.

Bao, Xiaoqi↗
NASA NTRS1981

Mixed spectral/finite difference approximations for slightly viscous flows

A numerical scheme is presented, which employs a standard finite difference approximation for the viscous terms in high Reynolds number flows, and resorts to pseudo-spectral methods for the advection terms to greatly reduce the major source of numerical error without dramatically increasing computational cost. The spectral/finite difference (SFD) method evaluates the advection term and second-order differences to evaluate the diffusion term. The fully finite difference (FFD) method with second-order central differences on both terms is also used. The SFD method can handle strong shocks and can outperform the FFD method at moderate viscosity.

Zang, T. A.↗
NASA NTRS1989

Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations

The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.

Hafez, Mohammed↗
NASA NTRS1983

Spectral methods for the Euler equations

Spectral methods for compressible flows are introduced in relation to finite difference and finite element techniques within the framework of the method of weighted residuals. Current spectral collocation methods are put in historical context. The basic concepts of both Fourier and Chebyshev spectral collocation methods are provided. Filtering strategies for both shock-fitting and shock-capturing approaches are also presented. Fourier shock capturing techniques are evaluated using a one-dimensional, periodic astrophysical 'nozzle' problem. Examples of shock-fitting approaches include a shock/acoustic wave interaction, shock/vortex interaction, and the classical blunt body problem. While the shock capturing spectral method does not yet show a clear advantage over second-order finite differences, equivalent accuracy can be obtained using shock fitting with far fewer grid points.

Hussaini, M. Y.↗
NASA NTRS1999

Advanced Electromagnetic Methods for Aerospace Vehicles

The imminent destructive threats of Lightning on helicopters and other airborne systems has always been a topic of great interest to this research grant. Previously, the lightning induced currents on the surface of the fuselage and its interior were predicted using the finite-difference time-domain (FDTD) method as well as the NEC code. The limitations of both methods, as applied to lightning, were identified and extensively discussed in the last meeting. After a thorough investigation of the capabilities of the FDTD, it was decided to incorporate into the numerical method a subcell model to accurately represent current diffusion through conducting materials of high conductivity and finite thickness. Because of the complexity of the model, its validity will be first tested for a one-dimensional FDTD problem. Although results are not available yet, the theory and formulation of the subcell model are presented and discussed here to a certain degree. Besides lightning induced currents in the interior of an aircraft, penetration of electromagnetic fields through apertures (e.g., windows and cracks) could also be devastating for the navigation equipment, electronics, and communications systems in general. The main focus of this study is understanding and quantifying field penetration through apertures. The simulation is done using the FDTD method and the predictions are compared with measurements and moment method solutions obtained from the NASA Langley Research Center. Cavity-backed slot (CBS) antennas or slot antennas in general have many applications in aircraft-satellite type of communications. These can be flushmounted on the surface of the fuselage and, therefore, they retain the aerodynamic shape of the aircraft. In the past, input impedance and radiation patterns of CBS antennas were computed using a hybrid FEM/MoM code. The analysis is now extended to coupling between two identical slot antennas mounted on the same structure. The predictions are performed using both the hybrid FEM/MoM and the FDTD NEWS code. The results are compared with each other as well as with measurements performed in the ElectroMagnetic Anechoic Chamber (EMAC) of ASU. In addition to self and mutual impedances versus frequency, the comparisons include mutual coupling S(sub 12) as a function of distance for various slot orientations.

Balanis, Constantine A.↗
NASA NTRSDate not supplied

A Numerical Method for Computing the State Transition Matrix Using Poincare Integral Invariants

The Poincare integral invariants describe the volumes of sets in Hamiltonian phase space. We use these invariants to derive a new numerical procedure for obtaining the state transition matrix (STM), which can be applied to both conservative and nonconservative systems. The method is analogous to a finite difference approximation of the STM, where perturbed states are numerically propagated along with the reference trajectory. We discuss the mathematical similarities between this new STM and existing methods, show numerical results for orbital motion and uncertainty propagation, and discuss new insights afforded by the Hamiltonian properties of phase flow.

state transition matrix↗
NASA NTRS1994

Aeroacoustic sensitivity analysis and optimal aeroacoustic design of turbomachinery blades

During the first year of the project, we have developed a theoretical analysis - and wrote a computer code based on this analysis - to compute the sensitivity of unsteady aerodynamic loads acting on airfoils in cascades due to small changes in airfoil geometry. The steady and unsteady flow though a cascade of airfoils is computed using the full potential equation. Once the nominal solutions have been computed, one computes the sensitivity. The analysis takes advantage of the fact that LU decomposition is used to compute the nominal steady and unsteady flow fields. If the LU factors are saved, then the computer time required to compute the sensitivity of both the steady and unsteady flows to changes in airfoil geometry is quite small. The results to date are quite encouraging, and may be summarized as follows: (1) The sensitivity procedure has been validated by comparing the results obtained by 'finite difference' techniques, that is, computing the flow using the nominal flow solver for two slightly different airfoils and differencing the results. The 'analytic' solution computed using the method developed under this grant and the finite difference results are found to be in almost perfect agreement. (2) The present sensitivity analysis is computationally much more efficient than finite difference techniques. We found that using a 129 by 33 node computational grid, the present sensitivity analysis can compute the steady flow sensitivity about ten times more efficiently that the finite difference approach. For the unsteady flow problem, the present sensitivity analysis is about two and one-half times as fast as the finite difference approach. We expect that the relative efficiencies will be even larger for the finer grids which will be used to compute high frequency aeroacoustic solutions. Computational results show that the sensitivity analysis is valid for small to moderate sized design perturbations. (3) We found that the sensitivity analysis provided important insight into how airfoils should be modified to improve their aeroelastic stability. Using this insight, we redesigned an aeroelastically unstable cascade to produce a stable cascade.

Hall, Kenneth C.↗
NASA NTRS1984

Structural sensitivity analysis: Methods, applications and needs

Innovative techniques applicable to sensitivity analysis of discretized structural systems are reviewed. The techniques include a finite difference step size selection algorithm, a method for derivatives of iterative solutions, a Green's function technique for derivatives of transient response, simultaneous calculation of temperatures and their derivatives, derivatives with respect to shape, and derivatives of optimum designs with respect to problem parameters. Computerized implementations of sensitivity analysis and applications of sensitivity derivatives are also discussed. Some of the critical needs in the structural sensitivity area are indicated along with plans for dealing with some of those needs.

Adelman, H. M.↗
NASA NTRS1991

A comparison of two closely-related approaches to aerodynamic design optimization

Two related methods for aerodynamic design optimization are compared. The methods, called the implicit gradient approach and the variational (or optimal control) approach, both attempt to obtain gradients necessary for numerical optimization at a cost significantly less than that of the usual black-box approach that employs finite difference gradients. While the two methods are seemingly quite different, they are shown to differ (essentially) in that the order of discretizing the continuous problem, and of applying calculus, is interchanged. Under certain circumstances, the two methods turn out to be identical. We explore the relationship between these methods by applying them to a model problem for duct flow that has many features in common with transonic flow over an airfoil. We find that the gradients computed by the variational method can sometimes be sufficiently inaccurate to cause the optimization to fail.

Shubin, G. R.↗
NASA NTRS1993

The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows

We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing Eulerian schemes in its use of operator-splitting and artificial viscosity, except that we solve the Lagrangian equations of motion with a predictor-corrector and then remap onto a fixed Eulerian grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector Lagrangian-remap code has great flexibility for application to a variety of astrophysical problems.

Lufkin, Eric A.↗
NASA NTRS1999

Sensitivity Analysis for Coupled Aero-structural Systems

A novel method has been developed for calculating gradients of aerodynamic force and moment coefficients for an aeroelastic aircraft model. This method uses the Global Sensitivity Equations (GSE) to account for the aero-structural coupling, and a reduced-order modal analysis approach to condense the coupling bandwidth between the aerodynamic and structural models. Parallel computing is applied to reduce the computational expense of the numerous high fidelity aerodynamic analyses needed for the coupled aero-structural system. Good agreement is obtained between aerodynamic force and moment gradients computed with the GSE/modal analysis approach and the same quantities computed using brute-force, computationally expensive, finite difference approximations. A comparison between the computational expense of the GSE/modal analysis method and a pure finite difference approach is presented. These results show that the GSE/modal analysis approach is the more computationally efficient technique if sensitivity analysis is to be performed for two or more aircraft design parameters.

Giunta, Anthony A.↗