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NASA NTRS2006

Polarization Rotation and the Third Stokes Parameter: The Effects of Spacecraft Attitude and Faraday Rotation

The third Stokes parameter of ocean surface brightness temperatures measured by the WindSat instrument is sensitive to the rotation angle between the polarization vectors at the ocean surface and the instrument. This rotation angle depends on the spacecraft attitude (roll, pitch, yaw) as well as the Faraday rotation of the electromagnetic radiation passing through the Earth's ionosphere. Analyzing the WindSat antenna temperatures, we find biases in the third Stokes parameter as function of the along-scan position of up to 1.5 K in all feedhorns. This points to a misspecification of the reported spacecraft attitude. A single attitude correction of -0.16deg roll and 0.18deg pitch for the whole instrument eliminates all the biases. We also study the effect of Faraday rotation at 10.7 GHz on the accuracy of the third Stokes parameter and the sea surface wind direction retrieval and demonstrate how this error can be corrected using values from the International Reference Ionosphere for the total electron content when computing Faraday rotation.

Meissner, Thomas↗

NASA NTRS2010

Global Mass Flux Solutions from GRACE: A Comparison of Parameter Estimation Strategies - Mass Concentrations Versus Stokes Coefficients

The differences between mass concentration (mas con) parameters and standard Stokes coefficient parameters in the recovery of gravity infonnation from gravity recovery and climate experiment (GRACE) intersatellite K-band range rate data are investigated. First, mascons are decomposed into their Stokes coefficient representations to gauge the range of solutions available using each of the two types of parameters. Next, a direct comparison is made between two time series of unconstrained gravity solutions, one based on a set of global equal area mascon parameters (equivalent to 4deg x 4deg at the equator), and the other based on standard Stokes coefficients with each time series using the same fundamental processing of the GRACE tracking data. It is shown that in unconstrained solutions, the type of gravity parameter being estimated does not qualitatively affect the estimated gravity field. It is also shown that many of the differences in mass flux derivations from GRACE gravity solutions arise from the type of smoothing being used and that the type of smoothing that can be embedded in mas con solutions has distinct advantages over postsolution smoothing. Finally, a 1 year time series based on global 2deg equal area mascons estimated every 10 days is presented.

Rowlands, D. D.↗

NASA NTRS2012

Large-Eddy / Reynolds-Averaged Navier-Stokes Simulations of a Dual-Mode Scramjet Combustor

Numerical simulations of reacting and non-reacting flows within a scramjet combustor configuration experimentally mapped at the University of Virginia s Scramjet Combustion Facility (operating with Configuration A ) are described in this paper. Reynolds-Averaged Navier-Stokes (RANS) and hybrid Large Eddy Simulation / Reynolds-Averaged Navier-Stokes (LES / RANS) methods are utilized, with the intent of comparing essentially blind predictions with results from non-intrusive flow-field measurement methods including coherent anti-Stokes Raman spectroscopy (CARS), hydroxyl radical planar laser-induced fluorescence (OH-PLIF), stereoscopic particle image velocimetry (SPIV), wavelength modulation spectroscopy (WMS), and focusing Schlieren. NC State's REACTMB solver was used both for RANS and LES / RANS, along with a 9-species, 19- reaction H2-air kinetics mechanism by Jachimowski. Inviscid fluxes were evaluated using Edwards LDFSS flux-splitting scheme, and the Menter BSL turbulence model was utilized in both full-domain RANS simulations and as the unsteady RANS portion of the LES / RANS closure. Simulations were executed and compared with experiment at two equivalence ratios, PHI = 0.17 and PHI = 0.34. Results show that the PHI = 0.17 flame is hotter near the injector while the PHI = 0.34 flame is displaced further downstream in the combustor, though it is still anchored to the injector. Reactant mixing was predicted to be much better at the lower equivalence ratio. The LES / RANS model appears to predict lower overall heat release compared to RANS (at least for PHI = 0.17), and its capability to capture the direct effects of larger turbulent eddies leads to much better predictions of reactant mixing and combustion in the flame stabilization region downstream of the fuel injector. Numerical results from the LES/RANS model also show very good agreement with OH-PLIF and SPIV measurements. An un-damped long-wave oscillation of the pre-combustion shock train, which caused convergence problems in some RANS simulations, was also captured in LES / RANS simulations, which were able to accommodate its effects accurately.

Fulton, Jesse A.↗

NASA NTRS2015

Entropy Stable Staggered Grid Spectral Collocation for the Burgers' and Compressible Navier-Stokes Equations

Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).

Carpenter, Mark H.↗

NASA NTRS2021

Stokes resolved differential temperature: an important metric of polarimetric precision in the long-wave infrared

In remote sensing, radiometric measurements taken in the mid-wave infrared and beyond (λ >3μm) are commonly reported in units of Kelvin by utilizing Planck’s radiation law to relate measured radiance and target brightness temperature (Tb). Thus, it is desirable to match this formalism in thermal polarimetry and report the unnormalized Stokes parameters in units of K instead of radiance (Wm−2sr−1). This approach also al-lows common performance metrics in long-wave infrared (LWIR) imaging such as Noise Equivalent DifferentialTemperature (NEDT) to be modified and extended to metrics of polarimetric accuracy and precision. However, since the relationship between measured radiance and Tb are non-linear, the conversion of I, Q, and U in units of radiance to Tb,Tb,Q, and Tb,U in K is ambiguous. As a solution a metric of performance for thermal linear Stokes polarimetry, the Stokes resolved differential temperature (SRDT), is introduced.

polarimetry↗

NASA NTRS1993

Multiblock Navier-Stokes solutions about the F/A-18 wing-LEX-fuselage configuration

Three-dimensional thin-layer Navier-Stokes computations are presented for the F/A-18 configuration. The modeled configuration includes an accurate surface representation of the fuselage, leading-edge extension (LEX), and wing, both with and without leading-edge flap deflection. A multiblock structured grid strategy is employed to decompose the computational flowfield domain around the subject configuration. Steady-state solutions are obtained from an algorithm that solves the compressible Navier-Stokes equations with an upwind-biased, flux-difference splitting approach. The results presented are based on a fully turbulent flow assumption, simulating the high Reynolds number flow conditions that correspond to a recent FI A-18 flight experiment. Good agreements between the computations and the flight test results are obtained for both surface flow patterns as well as surface pressure distributions. Furthermore, a correlation between the computed LEX vortex-core and the flight test results, observed by way of smoke visualization, is also presented.

Aircraft configurations↗

NASA NTRS2022

The Fourth Stokes Parameter for Geolocation in Passive Microwave Remote Sensing from Space

Polarimetric microwave radiometers such as SMAP are capable of measuring the fourth Stokes parameter in brightness temperature over the Earth surface. The value of this parameter is normally small but exhibits sharp spikes when the scene includes large differences in emission from the surface, such occur at land/water boundaries. In this manuscript, it is shown that these spikes can be used to accurately locate coastlines with potential application to geolocation in passive microwave remote sensing from space. Examples are presented using the L-band radiometer on SMAP, first with theory using calculations with the SMAP antenna pattern and orbit and then with SMAP measurements of the fourth Stokes parameter over Madagascar. Using the SMAP data, the coastline is located with a standard deviation less than 2 km. The results are consistent with the conventional approach used for geolocation of the SMAP radiometer footprint.

Passive Microwave Remote Sensing↗

NASA NTRS1972

Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner

Numerical solutions have been obtained for the supersonic, laminar flow over a two-dimensional compression corner. These solutions were obtained as steady-state solutions to the unsteady Navier-Stokes equations using the finite difference method of Brailovskaya, which has second-order accuracy in the spatial coordinates. Good agreement was obtained between the computed results and wall pressure distributions measured experimentally for Mach numbers of 4 and 6.06, and respective Reynolds numbers, based on free-stream conditions and the distance from the leading edge to the corner. In those calculations, as well as in others, sufficient resolution was obtained to show the streamline pattern in the separation bubble. Upstream boundary conditions to the compression corner flow were provided by numerically solving the unsteady Navier-Stokes equations for the flat plate flow field, beginning at the leading edge. The compression corner flow field was enclosed by a computational boundary with the unknown boundary conditions supplied by extrapolation from internally computed points.

Carter, J. E.↗

NASA NTRS1974

A Stokes' velocity photographic method for measuring the size distribution of aerosols

Aerosol particles are allowed to settle in a vertical glass walled vessel, and their settling velocity is determined by photographing them while the light entering the camera is being chopped at a known rate. The settling velocity of each particle can be determined from the photographs, and by applying the Stokes' law, one can calculate the radius of each particle. The Stokes' law for a sphere settling freely in a quiet medium is given. If the volume of the photographed region of the illumination is known, the aerosol number density and size distribution can be obtained. Experiments with alumina particles of given size distributions indicate that the method works accurately. One set of a typical experiment with 3.0-micrometer Al2O3 particles is presented, which shows that the measured size distribution peaks at approximately 3.0 micrometer.

Deepak, A.↗

NASA NTRS1974

Numerical solution of the steady-state Navier-Stokes equations for hypersonic flow about blunt axisymmetric bodies

The steady-state Navier-Stokes equations are solved for hypersonic flow about blunt axisymmetric bodies. The equations of motion are solved by successive approximations using an implicit finite-difference scheme. The results are compared with viscous shock-layer theory, experimental data, and time-dependent solutions of the Navier-Stokes equations. It is demonstrated that viscous shock-layer theory is sufficiently accurate for the range of flight conditions normally encountered by entry vehicles.

Anderson, E. C.↗

NASA NTRS1974

A finite element solution algorithm for the Navier-Stokes equations

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame.

Baker, A. J.↗

NASA NTRS1974

Computer extension and analytic continuation of Stokes' expansion for gravity waves

Stokes' infinitesimal-wave expansion for steady progressive free-surface waves has been extended to high order using a computer to perform the coefficient arithmetic. Stokes' expansion has been found to be incapable of yielding the highest wave for any value of the water depth since convergence is limited by a square-root branch-point some distance short of the maximum. By reformulating the problem using a different independent parameter, the highest waves are obtained correctly. Series summation and analytic continuation are facilitated by the use of Pade approximants. The method is valid in principle for any finite value of the wavelength and solutions of high accuracy can be obtained for most values of the wave height and water depth.

Schwartz, L. W.↗

NASA NTRS1975

A rigorous solution of the Navier-Stokes equations for unsteady viscous flow at high Reynolds numbers around oscillating airfoils

A method based on the Navier-Stokes equations was developed for analyzing the unsteady incompressible viscous flow around oscillating airfoils at high Reynolds numbers. The Navier-Stokes equations have been integrated in their classical Helmholtz vorticity transport equation form, and the instantaneous velocity field at each time step was determined by the solution of Poisson's equation. A refined finite element was utilized to allow for a conformable solution of the stream function and its first space derivatives at the element interfaces. A corresponding set of accurate boundary conditions was applied; thus obtaining a rigorous solution for the velocity field. The details of the computational procedure and examples of computed results describing the unsteady flow characteristics around the airfoil are presented.

Bratanow, T.↗

NASA NTRS1975

Development of an efficient computer code to solve the time-dependent Navier-Stokes equations

A research effort was conducted with the goal of reducing computer time of a Navier Stokes Computer Code for prediction of viscous flow fields about lifting bodies. A two-dimensional, time-dependent, laminar, transonic computer code (STOKES) was modified to incorporate a non-uniform timestep procedure. The non-uniform time-step requires updating of a zone only as often as required by its own stability criteria or that of its immediate neighbors. In the uniform timestep scheme each zone is updated as often as required by the least stable zone of the finite difference mesh. Because of less frequent update of program variables it was expected that the nonuniform timestep would result in a reduction of execution time by a factor of five to ten. Available funding was exhausted prior to successful demonstration of the benefits to be derived from the non-uniform time-step method.

Harp, J. L., Jr.↗

NASA NTRS1976

The relative merits of several numerical techniques for solving the compressible Navier-Stokes equations

Four explicit finite difference techniques designed to solve the time-dependent, compressible Navier Stokes equations are compared. These techniques are: (1) MacCormack, (2) modified Du Fort-Frankel, (3) modified hopscotch, and (4) Brailovskaya. The comparison was made numerically by solving the quasi-one dimensional Navier Stokes equations for the flow in a converging-diverging nozzle. Solutions with and without standing normal shock waves were computed for unit Reynolds numbers (based on total conditions) ranging from 45374 to 2269. The results indicate that all four techniques are comparable in accuracy; however, the modified hopscotch scheme is two to three times faster than the Brailovskaya and MacCormack schemes and three to six times faster than the modified Du Fort-Frankel scheme.

Holst, T. L.↗

NASA NTRS1976

Numerical solution of the steady-state Navier-Stokes equations for hypersonic flow about blunt axisymmetric bodies

Anderson, E. C.↗

NASA NTRS1978

The determination of gravity anomalies from geoid heights using the inverse Stokes' formula, Fourier transforms, and least squares collocation

A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.

Rummel, R.↗

NASA NTRS1979

Investigations of coherent anti-Stokes Raman spectroscopy /CARS/ for combustion diagnostics

Investigations of coherent anti-Stokes Raman spectroscopy (CARS) in a variety of flames are presented. Thermometry has received the primary emphasis in these studies, but species spectral and sensitivity studies will also be described. CARS is generated by mixing a 10 pps, frequency-doubled neodymium 'pump' laser with a spectrally broadband, laser-pumped, Stokes-shifted dye laser. This approach obviates the requirement to frequency scan the dye laser and generates the entire CARS spectrum with each pulse permitting, in principle, instantaneous measurements of medium properties. CARS spectra of N2, CO, O2, H2O, CO2 and CH4 in flames will be presented. In general these spectra exhibit very good agreement with computer synthesized spectra and permit measurements of temperature and species concentration. To illustrate the applicability of CARS to practical combustion diagnostics, CARS signatures from N2 have been employed to map the temperature field throughout a small, luminous, highly sooting propane diffusion flame

Eckbreth, A. C.↗