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NASA NTRS1997

On the Role of Resonances in Nonradial Pulsators

Resonances or near resonances are ubiquitous among the excited nonradial pulsation modes of variable stars and they must play an important role in determining their pulsational behavior. Here in a first step at nonlinear asteroseismology, we explore some of the consequences of resonances by means of the amplitude equation formalism. We show how parity and angular momentum constraints can be used to eliminate many of the possible nonlinear resonant couplings between modes (and multiplets of modes), and how the amplitude equations can thus be simplified. Even when we may not be able, nor wish, to make an ab initio computation of the values of the coupling coefficients, it is still possible to obtain constraints on the nature of the excited modes if a resonance between observed frequencies can be identified. Resonances can cause nonlinear frequency locking of modes. This means that the observed frequencies appear in exact resonance even though the linear frequencies are only approximately in resonance. The nonlinear frequency lock, when it occurs, it does so over a range of departures from linear resonance, and it is accompanied by constant pulsation amplitudes. The locked, nonlinear frequencies can differ noticeably from their nonresonant counterparts which are usually used in seismology. This is particularly true for multiplets of modes split by rotation. Beyond the regime of the frequency lock, amplitude and frequency modulations can appear in the pulsations. Far from the resonance condition one recovers the regime of steady pulsations with nonresonant frequencies for which the seismological studies, as they are presently carried out, are justified (provided furthermore, of course, that nonlinear frequency shifts are negligible). Success in identifying a resonance in an observed power spectrum depends on the quality of the data. While keeping this limitation in mind, ew discuss the possible existence of peculiar resonances the pulsations specific variable white dwarfs and delta Scuti stars.

Buchler, J. R.↗
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗
NASA NTRS2015

Use of North American and European Air Quality Networks to Evaluate Global Chemistry-Climate Modeling of Surface Ozone

We test the current generation of global chemistry-climate models in their ability to simulate observed, present-day surface ozone. Models are evaluated against hourly surface ozone from 4217 stations in North America and Europe that are averaged over 1 degree by 1 degree grid cells, allowing commensurate model-measurement comparison. Models are generally biased high during all hours of the day and in all regions. Most models simulate the shape of regional summertime diurnal and annual cycles well, correctly matching the timing of hourly (approximately 15:00 local time (LT)) and monthly (mid-June) peak surface ozone abundance. The amplitude of these cycles is less successfully matched. The observed summertime diurnal range (25 ppb) is underestimated in all regions by about 7 parts per billion, and the observed seasonal range (approximately 21 parts per billion) is underestimated by about 5 parts per billion except in the most polluted regions, where it is overestimated by about 5 parts per billion. The models generally match the pattern of the observed summertime ozone enhancement, but they overestimate its magnitude in most regions. Most models capture the observed distribution of extreme episode sizes, correctly showing that about 80 percent of individual extreme events occur in large-scale, multi-day episodes of more than 100 grid cells. The models also match the observed linear relationship between episode size and a measure of episode intensity, which shows increases in ozone abundance by up to 6 parts per billion for larger-sized episodes. We conclude that the skill of the models evaluated here provides confidence in their projections of future surface ozone.

diurnal variations↗
NASA NTRS1991

Annealing of linear birefringence in single-mode fiber coils - Application to optical fiber current sensors

Annealing procedures that greatly reduce linear birefringence in single-mode fiber coils are described. These procedures have been successfully applied to coils ranging from 5 mm to 10 cm in diameter and up to 200 or more turns. They involve temperature cycles that last 3-4 days and reach maximum temperatures of about 850 C. The residual birefringence and induced loss are minimized by proper selection of fiber. The primary application of these coils is optical fiber current sensors, where they yield small sensors that are more stable than those achieved by other techniques. A current sensor with a temperature stability of 8.4 x 10 to the -5th/K over the range from -75 to 145 C has been demonstrated. This is approximately 20 percent greater than the temperature dependence of the Verdet constant. Packaging degrades the stability, but a packaged sensor coil with a temperature stability of about 1.6 + 10 to the -4th/K over the range from -20 to 120 C has also been demonstrated.

Tang, Dingding↗
NASA NTRS1993

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

In this study involving advanced fluid flow codes, an incremental iterative formulation (also known as the delta or correction form) together with the well-known spatially-split approximate factorization algorithm, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For smaller 2D problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods are needed for larger 2D and future 3D applications, however, because direct methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioning of the coefficient matrix; this problem can be overcome when these equations are cast in the incremental form. These and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two sample airfoil problems: (1) subsonic low Reynolds number laminar flow; and (2) transonic high Reynolds number turbulent flow.

Taylor, Arthur C., III↗
NASA NTRS2015

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

state estimation↗
NASA NTRS2016

Photosynthetic Efficiency of Northern Forest Ecosystems Using a MODIS-Derived Photochemical Reflectance Index (PRI)

This study evaluates a direct remote sensing approach from space for the determination of ecosystem photosynthetic light use efficiency (LUE), through measurement of vegetation reflectance changes expressed with the Photochemical Reflectance Index (PRI). The PRI is a normalized difference index based on spectral changes at a physiologically active wavelength (approximately 531 nanometers) as compared to a reference waveband, and is only available from a very few satellites. These include the two Moderate-Resolution Imaging Spectroradiometers (MODIS) on the Aqua and Terra satellites each of which have a narrow (10-nanometer) ocean band centered at 531 nanometers. We examined several PRI variations computed with candidate reference bands, since MODIS lacks the traditional 570-nanometer reference band. The PRI computed using MODIS land band 1 (620-670 nanometers) gave the best performance for daily LUE estimation. Through rigorous statistical analyses over a large image collection (n equals 420), the success of relating in situ daily tower-derived LUE to MODIS observations for northern forests was strongly influenced by satellite viewing geometry. LUE was calculated from CO2 fluxes (moles per moles of carbon absorbed quanta) measured at instrumented Canadian Carbon Program flux towers in four Canadian forests: a mature fir site in British Columbia, mature aspen and black spruce sites in Saskatchewan, and a mixed deciduous/coniferous forest site in Ontario. All aspects of the viewing geometry had significant effects on the MODIS-PRI, including the view zenith angle (VZA), the view azimuth angle, and the displacement of the view azimuth relative to the solar principal plane, in addition to illumination related variables.Nevertheless, we show that forward scatter sector views (VZA, 16 degrees-45 degrees) provided the strongest relationships to daily LUE, especially those collected in the early afternoon by Aqua (r squared = 0.83, RMSE (root mean square error) equals 0.003 moles per moles of carbon absorbed quanta). Nadir (VZA, 0 degrees plus or minus 15 degrees) and backscatter views (VZA, −16 degrees to −45 degrees) had lower performance in estimating LUE (nadir: r squared approximately equal to 0.62-0.67; backscatter: r squared approximately equal to 0.54-0.59) and similar estimation error (RMSE equals 0.004-0.005).When directional effects were not considered, only a moderately successful MODIS-PRI vs. LUE relationship (r squared equals 0.34, RMSE equals 0.007) was obtained in the full dataset (all views & sites, both satellites), but site-specific relationships were able to discriminate between coniferous and deciduous forests. Overall, MODIS-PRI values from Terra (late morning) were higher than those from Aqua (early afternoon), before/after the onset of diurnal stress responses expressed spectrally. Therefore, we identified ninety-two Terra-Aqua "same day" pairs, for which the sum of Terra morning and Aqua afternoon MODIS-PRI values (PRI (sub sum) using all available directional observations was linearly correlated with daily tower LUE (r squared equals 0.622, RMSE equals 0.013) and independent of site differences or meteorological information. Our study highlights the value of off-nadir directional reflectance observations, and the value of pairing morning and afternoon satellite observations to monitor stress responses that inhibit carbon uptake in Canadian forest ecosystems. In addition, we show that MODIS-PRI values, when derived from either: (i) forward views only, or (ii) Terra/Aqua same day (any view) combined observations, provided more accurate estimates of tower-measured daily LUE than those derived from either nadir or backscatter views or those calculated by the widely used semi-operational MODIS GPP model (MOD17) which is based on a theoretical maximum LUE and environmental data. Consequently, we demonstrate the importance of diurnal as well as off-nadir satellite observations for detecting vegetation physiological processes.

Middleton, E. M.↗
NASA NTRS1993

Multibeam Laser Altimeter for Planetary Topographic Mapping

Laser altimetry provides an active, high-resolution, high-accuracy method for measurement of planetary and asteroid surface topography. The basis of the measurement is the timing of the roundtrip propagation of short-duration pulses of laser radiation between a spacecraft and the surface. Vertical, or elevation, resolution of the altimetry measurement is determined primarily by laser pulse width, surface-induced spreading in time of the reflected pulse, and the timing precision of the altimeter electronics. With conventional gain-switched pulses from solid-state lasers and nanosecond resolution timing electronics, submeter vertical range resolution is possible anywhere from orbital altitudes of approximately 1 km to altitudes of several hundred kilometers. Horizontal resolution is a function of laser beam footprint size at the surface and the spacing between successive laser pulses. Laser divergence angle and altimeter platform height above the surface determine the laser footprint size at the surface, while laser pulse repetition rate, laser transmitter beam configuration, and altimeter platform velocity determine the spacing between successive laser pulses. Multiple laser transmitters in a single laser altimeter instrument that is orbiting above a planetary or asteroid surface could provide across-track as well as along-track coverage that can be used to construct a range image (i.e., topographic map) of the surface. We are developing a pushbroom laser altimeter instrument concept that utilizes a linear array of laser transmitters to provide contiguous across-track and along-track data. The laser technology is based on the emerging monolithic combination of individual, 1-sq cm diode-pumped Nd:YAG laser pulse emitters. Details of the multi-emitter laser transmitter technology, the instrument configuration, and performance calculations for a realistic Discovery-class mission will be presented.

Garvin, J. B.↗
NASA NTRS1996

Methodology for Sensitivity Analysis, Approximate Analysis, and Design Optimization in CFD for Multidisciplinary Applications

An incremental iterative formulation together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. This formulation is also known as the 'delta' or 'correction' form. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioned coefficient matrix; this problem is overcome when these equations are cast in the incremental form. The methodology is successfully implemented and tested using an upwind cell-centered finite-volume formulation applied in two dimensions to the thin-layer Navier-Stokes equations for external flow over an airfoil. In three dimensions this methodology is demonstrated with a marching-solution algorithm for the Euler equations to calculate supersonic flow over the High-Speed Civil Transport configuration (HSCT 24E). The sensitivity derivatives obtained with the incremental iterative method from a marching Euler code are used in a design-improvement study of the HSCT configuration that involves thickness. camber, and planform design variables.

Taylor, Arthur C., III↗
NASA NTRS2011

Ares I-X In-Flight Modal Identification

Operational modal analysis is a procedure that allows the extraction of modal parameters of a structure in its operating environment. It is based on the idealized premise that input to the structure is white noise. In some cases, when free decay responses are corrupted by unmeasured random disturbances, the response data can be processed into cross-correlation functions that approximate free decay responses. Modal parameters can be computed from these functions by time domain identification methods such as the Eigenvalue Realization Algorithm (ERA). The extracted modal parameters have the same characteristics as impulse response functions of the original system. Operational modal analysis is performed on Ares I-X in-flight data. Since the dynamic system is not stationary due to propellant mass loss, modal identification is only possible by analyzing the system as a series of linearized models over short periods of time via a sliding time-window of short time intervals. A time-domain zooming technique was also employed to enhance the modal parameter extraction. Results of this study demonstrate that free-decay time domain modal identification methods can be successfully employed for in-flight launch vehicle modal extraction.

Bartkowicz, Theodore J.↗
NASA NTRS1988

Development of a unit cell for a Ge:Ga detector array

Two modules of gallium-doped germanium (Ge:Ga) infrared detectors with integrated multiplexing readouts and supporting drive electronics were designed and tested. This development investigated the feasibility of producing two-dimensional Ge:Ga arrays by stacking linear modules in a housing capable of providing uniaxial stress for enhanced long-wavelength response. Each module includes 8 detectors (1x1x2 mm) mounted to a sapphire board. The element spacing is 12 microns. The back faces of the detector elements are beveled with an 18 deg angle, which was proved to significantly enhance optical absorption. Each module includes a different silicon metal-oxide semiconductor field effect transistor (MOSFET) readout. The first circuit was built from discrete MOSFET components; the second incorporated devices taken from low-temperature integrated circuit multiplexers. The latter circuit exhibited much lower stray capacitance and improved stability. Using these switched-FET circuits, it was demonstrated that burst readout, with multiplexer active only during the readout period, could successfully be implemented at approximately 3.5 K.

Source record↗
NASA NTRS1986

A new approximate LU factorization scheme for the Reynolds-averaged Navier-Stokes equations

A new approximate LU factorization scheme is developed to solve the steady state Reynolds-averaged Navier-Stokes (NS) equations. Central differencing is used for both implicit and explicit operator and special care is taken to obtain well-conditioned factors on the implicit side. The scheme is then analyzed and optimized according to a simple linear analysis. It is unconditionally stable for the model hyperbolic equation in both two- and three-dimensions. However, the requirement for well-conditioned factors has essentially limited the effective time step the scheme can achieve. Supersonic and transonic three-dimensinal flows past a hemisphere cylinder are computed to demonstrate the convergence characteristics of the scheme. A good convergence rate is achieved for the inviscid case. Finally, an explicit eigenvector annihilation procedure is adopted successfully to remove the stiffness caused by the fine grid spacing for viscous flows.

Pan, D.↗
NASA NTRS2010

Suppressing Loss of Ions in an Atomic Clock

An improvement has been made in the design of a compact, highly stable mercury- ion clock to suppress a loss of ions as they are transferred between the quadrupole and higher multipole ion traps. Such clocks are being developed for use aboard spacecraft for navigation and planetary radio science. The modification is also applicable to ion clocks operating on Earth: indeed, the success of the modification has been demonstrated in construction and operation of a terrestrial breadboard prototype of the compact, highly stable mercury-ion clock. Selected aspects of the breadboard prototype at different stages of development were described in previous NASA Tech Briefs articles. The following background information is reviewed from previous articles: In this clock as in some prior ion clocks, mercury ions are shuttled between two ion traps, one a 16- pole linear radio-frequency trap, while the other is a quadrupole radio-frequency trap. In the quadrupole trap, ions are tightly confined and optical state selection from a 202Hg lamp is carried out. In the 16-pole trap, the ions are more loosely confined and atomic transitions are interrogated by use of a microwave beam at approximately 40.507 GHz. The trapping of ions effectively eliminates the frequency pulling that would otherwise be caused by collisions between clock atoms and the wall of a gas cell. The shuttling of the ions between the two traps enables separation of the state-selection process from the clock microwave-resonance process, so that each of these processes can be optimized independently of the other. This is similar to the operation of an atomic beam clock, except that with ions the beam can be halted and reversed as ions are shuttled back and forth between the two traps. When the two traps are driven at the same radio frequency, the strength of confinement can be reduced near the junction between the two traps, depending upon the relative phase of the RF voltage used to operate each of the two traps, and can cause loss of ions during each transit between the traps and thereby cause loss of the 40.507-GHz ion-clock resonance signal. The essence of the modification is to drive the two traps at different frequencies typically between 1.5 and 2 MHz for the quadrupole trap and a frequency a few hundred kHz higher for the 16- pole trap. A frequency difference of a few hundred kHz ensures that the ion motion caused by the trapping electric fields is small relative to the diameter of the traps. Unlike in the case in which both traps are driven at the same frequency, the trapping electric fields near the junction are not zero at all times; instead, the regions of low electric field near the junction open and close at the difference frequency. An additional benefit of making the 16-pole trap operate at higher frequency is that the strength or depth of the multipole trap can be increased independent of the quadrupole ion trap.

Prestage, John↗
NASA NTRS1985

Errors in reduction methods

A mathematical basis is given for comparing the relative merits of various techniques used to reduce the order of large linear and nonlinear dynamics problems during their numerical integration. In such techniques as Guyan-Irons, path derivatives, selected eigenvectors, Ritz vectors, etc., the nth order initial value problem of /y(dot) = f(y) for t greater than 0, y(0) given/ is typically reduced to the mth order (m is much less than n) problem of /z(dot) = g(z) for t greater than 0, z(0) given/ by the transformation y = Pz where P changes from technique to technique. This paper gives an explicit approximate expression for the reduction error e-i in terms of P and the Jacobian of f. It is shown that: (a) reduction techniques are more accurate when the time rate of change of the response y is relatively small; (b) the change in response between two successive stations contributes to the errors at future stations after the change in response is transformed by a filtering matrix H, defined in terms of P; (c) the error committed at a station propagates to future stations by a mixing and scaling matrix G, defined in terms of P, Jacobian and of f, and time increment h. The paper discusses the conditions under which the reduction errors may be minimized and gives guidelines for selecting the reduction basis vector, i.e., the columns of P.

Utku, S.↗
NASA NTRS1995

Numerical magetohydrodynamics in astronphysics: Algorithm and tests for one-dimensional flow`

We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the total variation diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. We also describe a non-linear Riemann solver for ideal MHD, which includes rarefractions as well as shocks. The numerical code and the Riemann solver have been used to test each other. Extensive tests encompassing all the possible ideal MHD structures with planar symmetries (i.e., one-dimensional flows) are presented. These include those for which the field structure is two dimensional (i.e., those flows often called '1 + 1/2 dimensional') as well as those for which the magnetic field plane rotates (i.e., those flows often called '1 + 1/2 + 1/2 dimensional'). Results indicate that the code can resolve strong fast, slow, and magnetosonic shocks within two to four cells, but more cells are required if shocks become weak. With proper steepening, we could resolve rotational discontinuities within three to five cells. However, without successful implementation of steepening, contact discontinuities are resolved with approximately 10 cells and tangential discountinuities are resolved with approximately 15 cells. Out tests confirm that slow compound structures with tow-dimensional magnetic fields are composed of intermediate shocks (so-called 2-4 intermediate shocks) followed by slow rarefaction waves. Finally, tests demostrate that in two-dimensional magnetohydrodynamics, fast compound structures, which are composed of intermediate shocks (so-called 1-3 intermediate shocks) preceeded by fast rarefaction waves, are also possible.

Ryu, Dongsu↗
NASA NTRS1998

Flight Testing the Linear Aerospike SR-71 Experiment (LASRE)

The design of the next generation of space access vehicles has led to a unique flight test that blends the space and flight research worlds. The new space vehicle designs, such as the X-33 vehicle and Reusable Launch Vehicle (RLV), are powered by linear aerospike rocket engines. Conceived of in the 1960's, these aerospike engines have yet to be flown, and many questions remain regarding aerospike engine performance and efficiency in flight. To provide some of these data before flying on the X-33 vehicle and the RLV, a spacecraft rocket engine has been flight-tested atop the NASA SR-71 aircraft as the Linear Aerospike SR-71 Experiment (LASRE). A 20 percent-scale, semispan model of the X-33 vehicle, the aerospike engine, and all the required fuel and oxidizer tanks and propellant feed systems have been mounted atop the SR-71 airplane for this experiment. A major technical objective of the LASRE flight test is to obtain installed-engine performance flight data for comparison to wind-tunnel results and for the development of computational fluid dynamics-based design methodologies. The ultimate goal of firing the aerospike rocket engine in flight is still forthcoming. An extensive design and development phase of the experiment hardware has been completed, including approximately 40 ground tests. Five flights of the LASRE and firing the rocket engine using inert liquid nitrogen and helium in place of liquid oxygen and hydrogen have been successfully completed.

Stephen Corda↗
NASA NTRS2014

Lightning Current Measurement with Fiber-Optic Sensor

A fiber-optic current sensor is successfully developed with many potential applications for electric current measurement. Originally developed for in-flight lightning measurement, the sensor utilizes Faraday Effect in an optical fiber. The Faraday Effect causes linear light polarization in a fiber to rotate when the fiber is exposed to a magnetic field. The polarization change is detected using a reflective polarimetric scheme. Forming fiber loops and applying Ampere's law, measuring the total light rotation results in the determination of the total current enclosed. The sensor is conformable to complex structure geometry. It is also non-conductive and immune to electromagnetic interference, saturation or hysteresis. Installation is non-intrusive, and the sensor can be safely routed through flammable areas. Two similar sensor systems are described in this paper. The first system operates at 1310nm laser wavelength and is capable of measuring approximately 300 A - 300 kA, a 60 dB range. Laboratory validation results of aircraft lighting direct and in-direct effect current amplitudes are reported for this sensor. The second system operates at 1550nm wavelength and can measure about 400 A - 400 kA. Triggered-lightning measurement data are presented for this system. Good results are achieved in all cases.

Nguyen, Truong X.↗