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NASA NTRS2017

CLASP2: The Chromospheric LAyer Spectro-Polarimeter

A major remaining challenge for heliophysicsis to decipher the magnetic structure of the chromosphere, due to its "large role in defining how energy is transported into the corona and solar wind" (NASA's Heliophysics Roadmap). Recent observational advances enabled by the Interface Region Imaging Spectrometer (IRIS) have revolutionized our view of the critical role this highly dynamic interface between the photosphere and corona plays in energizing and structuring the outer solar atmosphere. Despite these advances, a major impediment to better understanding the solar atmosphere is our lack of empirical knowledge regarding the direction and strength of the magnetic field in the upper chromosphere. Such measurements are crucial to address several major unresolved issues in solar physics: for example, to constrain the energy flux carried by the Alfven waves propagating through the chromosphere (De Pontieuet al., 2014), and to determine the height at which the plasma Beta = 1 transition occurs, which has important consequences for the braiding of magnetic fields (Cirtainet al., 2013; Guerreiroet al., 2014), for propagation and mode conversion of waves (Tian et al., 2014a; Straus et al., 2008) and for non-linear force-free extrapolation methods that are key to determining what drives instabilities such as flares or coronal mass ejections (e.g.,De Rosa et al., 2009). The most reliable method used to determine the solar magnetic field vector is the observation and interpretation of polarization signals in spectral lines, associated with the Zeeman and Hanle effects. Magnetically sensitive ultraviolet spectral lines formed in the upper chromosphere and transition region provide a powerful tool with which to probe this key boundary region (e.g., Trujillo Bueno, 2014). Probing the magnetic nature of the chromosphere requires measurement of the Stokes I, Q, U and V profiles of the relevant spectral lines (of which Q, U and V encode the magnetic field information).

Chromosphere↗

NASA NTRS2017

CLASP2: The Chromospheric LAyer Spectro-Polarimeter

A major remaining challenge for heliophysicsis to decipher the magnetic structure of the chromosphere, due to its 'large role in defining how energy is transported into the corona and solar wind' (NASA's Heliophysics Roadmap). Recent observational advances enabled by the Interface Region Imaging Spectrometer (IRIS) have revolutionized our view of the critical role this highly dynamic interface between the photosphere and corona plays in energizing and structuring the outer solar atmosphere. Despite these advances, a major impediment to better understanding the solar atmosphere is our lack of empirical knowledge regarding the direction and strength of the magnetic field in the upper chromosphere. Such measurements are crucial to address several major unresolved issues in solar physics: for example, to constrain the energy flux carried by the Alfven waves propagating through the chromosphere (De Pontieuet al., 2014), and to determine the height at which the plasma β = 1 transition occurs, which has important consequences for the braiding of magnetic fields (Cirtainet al., 2013; Guerreiroet al., 2014), for propagation and mode conversion of waves (Tian et al., 2014a; Straus et al., 2008) and for non-linear force-free extrapolation methods that are key to determining what drives instabilities such as flares or coronal mass ejections (e.g., De Rosa et al., 2009). The most reliable method used to determine the solar magnetic field vector is the observation and interpretation of polarization signals in spectral lines, associated with the Zeeman and Hanle effects. Magnetically sensitive ultraviolet spectral lines formed in the upper chromosphere and transition region provide a powerful tool with which to probe this key boundary region (e.g., Trujillo Bueno, 2014). Probing the magnetic nature of the chromosphere requires measurement of the Stokes I, Q, U and V profiles of the relevant spectral lines (of which Q, U and V encode the magnetic field information).

Solar; Chromosphere; Polarization↗

NASA NTRS1994

VAPEPS Management Center

A VibroAcoustic Payload Environment Prediction System (VAPEPS) Management Center is established and being maintained at JPL. VAPEPS is a computer program that utilizes statistical energy analysis (SEA) theory and SEA extrapolation methods to predict the vibroacoustic environments of complex systems. The program is commonly utilized to establish random vibration and acoustic test requirements for aerospace components exposed to launch environments. It can also be used in the payload or launch vehicle design process for control or mitigation of the launch or on-orbit vibration and acoustic environments, as well as to calculate acoustically induced stresses in structures such as solar panels and reflectors.

VAPEPS↗

NASA NTRS1994

VAPEPS Management Center

VAPEPS is a computer program that utilizes statistical energy analysis (SEA) theory and SEA extrapolation methods to predict the vibroacoustic environments in complex systems.

vibroacoustic↗

NASA NTRSDate not supplied

Space-based UV Spectropolarimetry for Chromospheric Magnetic Field Measurements

High-resolution observations with space-and ground-based telescopes, along with advanced numerical modeling, have highlighted the intricate coupling between the chromosphere, transition region, and corona, and the critical role the chromosphere plays in the mass and energy balance of the outer solar atmosphere. Despite these recent advances, a major impediment to better understanding the solar atmosphere is our lack of empirical knowledge regarding the direction and strength of the magnetic field in the upper chromosphere (Decadal Survey, 2012). Such measurements are crucial to address several major unresolved issues in solar physics: for example, to constrain the energy flux carried by the Alfvén waves propagating through the chromosphere, and to determine the height at which the plasma β = 1 transition occurs, which has important consequences for the braiding of magnetic fields, for propagation and mode conversion of waves and for non-linear force-free extrapolation methods that are key to determining what drives instabilities such as flares or coronal mass ejections. Probing the magnetic nature of the Sun’s atmosphere requires measurement of the Stokes I, Q, U and V profiles of relevant spectral lines (of which Q, U and V encode the magnetic field information). Many of the magnetically sensitive lines formed in the chromosphere and transition region are in the ultraviolet spectrum, necessitating observations above the absorbing terrestrial atmosphere. The Chromospheric Layer Spectro-Polarimeter (“CLASP2”) sounding rocket was flown successfully in April 2019, as a follow-on to the successful flight in September 2015 of the Chromospheric Lyman-Alpha Spectro-Polarimeter (“CLASP1”). In October of 2021, we re-flew the CLASP2 experiment with a modified observing program to further demonstrate the maturity of the UV spectropolarimetry techniques, and readiness for development into a satellite observatory. During the reflight, called “CLASP2.1”, the spectrograph slit was scanned across an active region plage to acquire a two-dimensional map of Stokes V/I, to demonstrate the ability of UV spectropolarimetry to yield chromospheric magnetic fields over a large area.

David E McKenzie↗

NASA NTRS1984

An analysis of shock coalescence including three-dimensional effects with application to sonic boom extrapolation

A method for analyzing shock coalescence which includes three dimensional effects was developed. The method is based on an extension of the axisymmetric solution, with asymmetric effects introduced through an additional set of governing equations, derived by taking the second circumferential derivative of the standard shock equations in the plane of symmetry. The coalescence method is consistent with and has been combined with a nonlinear sonic boom extrapolation program which is based on the method of characteristics. The extrapolation program, is able to extrapolate pressure signatures which include embedded shocks from an initial data line in the plane of symmetry at approximately one body length from the axis of the aircraft to the ground. The axisymmetric shock coalescence solution, the asymmetric shock coalescence solution, the method of incorporating these solutions into the extrapolation program, and the methods used to determine spatial derivatives needed in the coalescence solution are described. Results of the method are shown for a body of revolution at a small, positive angle of attack.

Darden, C. M.↗

NASA NTRS1990

A comparison between progressive extension method (PEM) and iterative method (IM) for magnetic field extrapolations in the solar atmosphere

This paper presents a comparison between two numerical methods for the extrapolation of nonlinear force-free magnetic fields, viz the Iterative Method (IM) and the Progressive Extension Method (PEM). The advantages and disadvantages of these two methods are summarized, and the accuracy and numerical instability are discussed. On the basis of this investigation, it is claimed that the two methods do resemble each other qualitatively.

Wu, S. T.↗

NASA NTRS2014

Interpolation Method Needed for Numerical Uncertainty

Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors.

Groves, Curtis E.↗

NASA NTRS2014

Interpolation Method Needed for Numerical Uncertainty Analysis of Computational Fluid Dynamics

Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors in an unstructured grid, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors. Nomenclature

CFD↗

NASA NTRS1977

A critical study of higher-order numerical methods for solving the boundary-layer equations

A fourth-order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations. The efficiency of the present method is compared with other two-point and three-point higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, and the three-point spline methods. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.

Wornom, S. F.↗

NASA NTRS1978

Application of higher-order numerical methods to the boundary-layer equations

A fourth-order method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations for both attached and separated flows. The efficiency of the present method is compared with other higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, the three-point spline methods, and a modified finite-element method. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.

Wornom, S. F.↗

NASA NTRS1978

Critical study of higher order numerical methods for solving the boundary-layer equations

A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.

Wornom, S. F.↗

NASA NTRS1980

Study of the vortex conditions of wings with large sweepback by extrapolation of the Jones method

The pockets of separation originating on the leading edges are surrounded by vortex sheets. Their configuration and intensity were determined by four conditions with the JONES approximation, which is itself corrected by a simple logic. Field pressures and stresses were computed for different cases and are compared with test results (pure deltas, swallow tails, truncations, strakes, ducks, fuselage).

Hirsch, P.↗

NASA NTRS1992

Schroedinger's radial equation - Solution by extrapolation

A high-accuracy numerical method for the solution of a 1D Schroedinger equation that is suitable for a diatomic molecule, obtained by combining a finite-difference method with iterative extrapolation to the limit, is presently shown to have several advantages over more conventional methods. Initial guesses for the term values are obviated, and implementation of the algorithm is straightforward. The method is both less sensitive to round-off error, and faster than conventional methods for equivalent accuracy. These advantages are illustrated through the solution of Schroedinger's equation for a Morse potential function suited for HCl and a numerically derived Rydberg-Klein-Rees potential function for the X 1Sigma(+) state of CO.

Goorvitch, D.↗

NASA NTRS2017

Mixed Convection Blowoff Limits as a Function of Oxygen Concentration and Upward Forced Stretch Rate for Burning Pmma Rods of Various Sizes

Normal gravity flame blowoff limits in an axisymmetric pmma rod geometry in upward axial stagnation flow are compared with microgravity Burning and Suppression of Solids II (BASS-II) results recently obtained aboard the International Space Station. This testing utilized the same BASS-II concurrent rod geometry, but with the addition of normal gravity buoyant flow. Cast polymethylmethacrylate (pmma) rods of diameters ranging from 0.635 cm to 3.81 cm were burned at oxygen concentrations ranging from 14 to 18 by volume. The forced flow velocity where blowoff occurred was determined for each rod size and oxygen concentration. These blowoff limits compare favorably with the BASS-II results when the buoyant stretch is included and the flow is corrected by considering the blockage factor of the fuel. From these results, the normal gravity blowoff boundary for this axisymmetric rod geometry is determined to be linear, with oxygen concentration directly proportional to flow speed. We describe a new normal gravity upward flame spread test method which extrapolates the linear blowoff boundary to the zero stretch limit to resolve microgravity flammability limits, something current methods cannot do. This new test method can improve spacecraft fire safety for future exploration missions by providing a tractable way to obtain good estimates of material flammability in low gravity.

blowoff↗

NASA NTRS1956

Extrapolation techniques applied to matrix methods in neutron diffusion problems

A general matrix method is developed for the solution of characteristic-value problems of the type arising in many physical applications. The scheme employed is essentially that of Gauss and Seidel with appropriate modifications needed to make it applicable to characteristic-value problems. An iterative procedure produces a sequence of estimates to the answer; and extrapolation techniques, based upon previous behavior of iterants, are utilized in speeding convergence. Theoretically sound limits are placed on the magnitude of the extrapolation that may be tolerated. This matrix method is applied to the problem of finding criticality and neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron-diffusion equations is treated. Results for this example are indicated.

Mccready, Robert R↗

NASA NTRS2016

Correlation of Normal Gravity Mixed Convection Blowoff Limits with Microgravity Forced Flow Blowoff Limits

The axisymmetric rod geometry in upward axial stagnation flow provides a simple way to measure normal gravity blowoff limits to compare with microgravity Burning and Suppression of Solids - II (BASS-II) results recently obtained aboard the International Space Station. This testing utilized the same BASS-II concurrent rod geometry, but with the addition of normal gravity buoyant flow. Cast polymethylmethacrylate (PMMA) rods of diameters ranging from 0.635 cm to 3.81 cm were burned at oxygen concentrations ranging from 14 to 18% by volume. The forced flow velocity where blowoff occurred was determined for each rod size and oxygen concentration. These blowoff limits compare favorably with the BASS-II results when the buoyant stretch is included and the flow is corrected by considering the blockage factor of the fuel. From these results, the normal gravity blowoff boundary for this axisymmetric rod geometry is determined to be linear, with oxygen concentration directly proportional to flow speed. We describe a new normal gravity 'upward flame spread test' method which extrapolates the linear blowoff boundary to the zero stretch limit in order to resolve microgravity flammability limits-something current methods cannot do. This new test method can improve spacecraft fire safety for future exploration missions by providing a tractable way to obtain good estimates of material flammability in low gravity.

microgravity↗

NASA NTRS1989

Interplanetary observational constraints on Alfven wave acceleration of the solar wind

Spacecraft and interplanetary remote sensing observations of wave spectra are used to constrain the possible role of Alfven waves in the acceleration of high-speed streams in the solar wind. The observations suggest a method for extrapolating the wave energy flux near 1 AU back to the sun in a way that accounts for dissipation. Applying this method both for typical parameters and in the case of a well-studied high-speed stream leads to the conclusion that the Alfven waves observed in the solar wind were not sufficiently energetic near the sun to accelerate the streams.

Roberts, D. A.↗