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Results for “Separation of variables”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Variable-temperature cryogenic trap for the separation of gas mixtures

The paper describes a continuous variable-temperature U-shaped cold trap which can both purify vacuum-line combustion products for subsequent stable isotopic analysis and isolate the methane and ethane constituents of natural gases. The canister containing the trap is submerged in liquid nitrogen, and, as the gas cools, the gas mixture components condense sequentially according to their relative vapor pressures. After the about 12 min required for the bottom of the trap to reach the liquid-nitrogen temperature, passage of electric current through the resistance wire wrapped around the tubing covering the U-trap permits distillation of successive gas components at optimal temperatures. Data on the separation achieved for two mixtures, the first being typical vacuum-line combustion products of geochemical samples such as rocks and the second being natural gas, are presented, and the thermal behavior and power consumption are reported.

Des Marais, D. J.↗
NASA NTRS1991

Photon-assisted resonant tunneling through variably spaced superlattice energy filters

The observation of photon-assisted resonant tunneling in a multiple quantum well structure composed of doped quantum wells separated by variably space superlattice energy filters is reported. Electrons confined in the quantum wells are excited to the second quantized state by intersubband absorption of incident infrared radiation and are subsequently emitted through the filters under appropriate bias conditions. This is manifested by a distinct peak, with an associated negative differential photoconductance, in the photocurrent versus bias voltage characteristic at low temperatures.

Larsson, A.↗
NASA NTRS2014

Multi-point Adjoint-Based Design of Tilt-Rotors in a Noninertial Reference Frame

Optimization of tilt-rotor systems requires the consideration of performance at multiple design points. In the current study, an adjoint-based optimization of a tilt-rotor blade is considered. The optimization seeks to simultaneously maximize the rotorcraft figure of merit in hover and the propulsive efficiency in airplane-mode for a tilt-rotor system. The design is subject to minimum thrust constraints imposed at each design point. The rotor flowfields at each design point are cast as steady-state problems in a noninertial reference frame. Geometric design variables used in the study to control blade shape include: thickness, camber, twist, and taper represented by as many as 123 separate design variables. Performance weighting of each operational mode is considered in the formulation of the composite objective function, and a build up of increasing geometric degrees of freedom is used to isolate the impact of selected design variables. In all cases considered, the resulting designs successfully increase both the hover figure of merit and the airplane-mode propulsive efficiency for a rotor designed with classical techniques.

Jones, William T.↗
NASA NTRS1993

Observations on the long-period variability of the Gulf Stream downstream of Cape Hatteras

To examine the long-period variability of the Gulf Stream, sea level residuals relative to a 2-year mean sea level in the Gulf Stream downstream of Cape Hatteras (between 75 deg W and 60 deg W longitude) are used. Residuals, as derived from Geosat altimetry between November 1986 and December 1988, were gridded in space and time at a temporal resolution of 10 days and spatial resolution of 1/4 deg. Complex empirical orthogonal function (CEOF) analysis was applied to the data set to extract the spatially correlated signal with the original data subsampled to 1/2 deg. In addition to determining the space-time scales and propagation characterisitics of the different modes, wavenumber-frequency spectral techniques were used to separate the variability into propagating and stationary components. The CEOF technique applied to the data set indicated that the first four CEOF modes accounted for 60% of the variability and were found to be above the noise leve 99% of the time. CEOF 1 was associated with westward propagation at 5 km/d at a wavelength of 2000 km and eastward propagation at 1-2 km/d centered at a 500-km wavelength. This first CEOF is in good agreement with thin-jet equivalent barotropic models which predict westward propagation for wavelengths greater than 1130 km. A deflection of the wavelike pattern at 65 deg W also indicates a possible topographic effect. A simple scaling of the effect of topography indicates that for length scales longer than the internal Rossby radius of deformation, the topographic term is at least of the same order of magnitude as the beta effect. The second CEOF was more broadbanded in wavenumber space, with eastward propagation occurring in a wavenumber-frequency band between 300 and 1400 km and 0.5 and 2.0 cycles/yr. The third CEOF is similar in structure to the first, but with less energy. CEOF 4 was clearly identifiable with higher frequencies than the first three with westward propagation at 4 km/d. The spatial location of this mode along with the westward propagation indicates possible influences from eddy-stream interactions. Thus topography, Rossby wave dynamics and eddy-stream interactions all appear to have a significant role in determining the space-time scales and propagation properties of the long-period response of sea level in the Gulf Stream.

Vazquez, Jorge↗
NASA NTRS2021

Identifying Meteorological Influences on Marine Low Cloud Mesoscale Morphology Using Satellite Classifications

Marine low cloud mesoscale morphology in the southeastern Pacific Ocean is analyzed using a large dataset of machine-learning generated classifications spanning three years. Meteorological variables and cloud properties are composited 10by mesoscale cloud type, showing distinct meteorological regimes of marine low cloud organization from the tropics to the midlatitudes. The presentation of mesoscale cellular convection, with respect to geographic distribution, boundary layer structure, and large-scale environmental conditions, agrees with prior knowledge. Two tropical and subtropical cumuliform boundary layer regimes, suppressed cumulus and clustered cumulus, are studied in detail. The patterns in precipitation, circulation, column water vapor, and cloudiness are consistent with the representation of marine shallow mesoscale convective 15 self-aggregation by large eddy simulations of the boundary layer. Although they occur under similar large-scale conditions, the suppressed and clustered low cloud types are found to be well-separated by variables associated with low-level mesoscale circulation, with surface wind divergence being the clearest discriminator between them, whether reanalysis or satellite observations are used. Clustered regimes are associated with surface convergence and suppressed regimes are associated with surface divergence.

Johannes Mohrmann↗
NASA NTRS2001

High Order Difference Method for Low Mach Number Aeroacoustics

A high order finite difference method with improved accuracy and stability properties for computational aeroacoustics (CAA) at low Mach numbers is proposed. The Euler equations are split into a conservative and a symmetric non- conservative portion to allow the derivation of a generalized energy estimate. Since the symmetrization is based on entropy variables, that splitting of the flux derivatives is referred to as entropy splitting. Its discretization by high order central differences was found to need less numerical dissipation than conventional conservative schemes. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the split Euler equations are formulated in perturbation form. The unknowns are the small changes of the conservative variables with respect to their large stagnation values. All nonlinearities and the conservation form of the conservative portion of the split flux derivatives can be retained, while cancellation errors are avoided with its discretization opposed to the conventional conservative form. The finite difference method is third-order accurate at the boundary and the conventional central sixth-order accurate stencil in the interior. The difference operator satisfies the summation by parts property analogous to the integration by parts in the continuous energy estimate. Thus, strict stability of the difference method follows automatically. Spurious high frequency oscillations are suppressed by a characteristic-based filter similar to but without limiter. The time derivative is approximated by a 4-stage low-storage second-order explicit Runge-Kutta method. The method has been applied to simulate vortex sound at low Mach numbers. We consider the Kirchhoff vortex, which is an elliptical patch of constant vorticity rotating with constant angular frequency in irrotational flow. The acoustic pressure generated by the Kirchhoff vortex is governed by the 2D Helmholtz equation, which can be solved analytically using separation of variables.

Mueller, B.↗
NASA NTRS1960

Thermal-Fatigue Crack-Growth Characteristics and Mechanical Strain Cycling Behavior of A-286 Discaloy, and 16-25-6 Austenitic Steels

Thermal-fatigue crack-growth characteristics of notched- and unnotched-disk specimens of A-286, Discaloy, hot-cold worked 16-25-6, and overaged 16-25-6 were experimentally studied. Separately controlled variables were total strain range (0.0043 to 0.0079 in./in.), maximum cycle temperature (1300 and 1100 F), and hold time at maximum temperature (O and 5 min). A limited number of mechanical, push-pull, constant-strain cycle tests at room temperature were made using notched and un-notched bars of the same materials. In these tests the number of cycles to failure as well as the variation of load change with accumulated cycles was measured, and the effects of mean stress were observed. Constant-strain-range mechanical-fatigue tests at room temperature revealed notched-bar fatigue life to be strongly influenced by mean stress. For a specific strain range, the longest fatigue life was always found to be associated with the least-tensile (or most compressive) mean stress. By defining thermal-fatigue life as the number of cycles required to produce a crack area of 6000 square mils, the relative thermal-fatigue resistances of the test materials were established. Notched-disk specimens of A-286 and Discaloy steels exhibited longer fatigue lives than either hot-cold worked or overaged 16-25-6. On the other hand, unnotched-disk specimens of Discaloy and hot-cold worked 16-25-6 had longer lives than A-286 and overaged 16-25-6. Separation of the crack-growth data into microstage and macrostage periods revealed that the macrostage period accounted for the greatest part of the difference among materials when tested in the notched configuration, while the microstage was largely responsible for the differences encountered in unnotched disks.

Smith, Robert W.↗
NASA NTRS1974

Multiple eigenvalues of sound-absorbing circular and annular ducts

Eigenvalue equations of the form D(lambda) = 0 are studied for acoustic modes in circular and annular ducts without flow. The ducts have locally reacting walls with arbitrary wall admittance. It is shown that circular ducts may have double eigenvalues, or wall admittances where both D(lambda) and D prime (lambda) are zero. These double eigenvalues are formed by the coalescence of the lowest-order eigenfunction with some higher-order eigenfunction. The eigenfunctions, or acoustic modes, associated with the double eigenvalues are found to be orthogonal to themselves so that the standard expansion formula for the acoustic field, which is obtained from a separation-of-variables analysis, is invalid. An alternate expansion formula for the acoustic field is derived. This alternate formula shows that the coalesced acoustic mode is linearly amplified by the transmission distance and exponentially attenuated at the expected rate. The expansion formula also reveals a new eigenfunction, or acoustic mode, which is exponentially attenuated at the same rate as the coalesced eigenfunction.

Zorumski, W. E.↗
NASA NTRS1974

Application of modern control theory to scheduling and path-stretching maneuvers of aircraft in the near terminal area

A design concept of the dynamic control of aircraft in the near terminal area is discussed. An arbitrary set of nominal air routes, with possible multiple merging points, all leading to a single runway, is considered. The system allows for the automated determination of acceleration/deceleration of aircraft along the nominal air routes, as well as for the automated determination of path-stretching delay maneuvers. In addition to normal operating conditions, the system accommodates: (1) variable commanded separations over the outer marker to allow for takeoffs and between successive landings and (2) emergency conditions under which aircraft in distress have priority. The system design is based on a combination of three distinct optimal control problems involving a standard linear-quadratic problem, a parameter optimization problem, and a minimum-time rendezvous problem.

Athans, M.↗
NASA NTRS1975

Dual frequency scatterometer measurement of ocean wave height

A technique for remotely measuring wave height averaged over an area of the sea surface was developed and verified with a series of aircraft flight experiments. The measurement concept involves the cross correlation of the amplitude fluctuations of two monochromatic reflected signals with variable frequency separation. The signal reflected by the randomly distributed specular points on the surface is observed in the backscatter direction at nadir incidence angle. The measured correlation coefficient is equal to the square of the magnitude of the characteristic function of the specular point height from which RMS wave height can be determined. The flight scatterometer operates at 13.9 GHz and 13.9 - delta f GHz with a maximum delta f of 40 MHz. Measurements were conducted for low and moderate sea states at altitudes of 2, 5, and 10 thousand feet. The experimental results agree with the predicted decorrelation with frequency separation and with off-nadir incidence angle.

Johnson, J. W.↗
NASA NTRS1974

Geodesic synchrotron radiation in the Kerr geometry by the method of asymptotically factorized Green's functions

The scalar, electromagnetic, and gravitational geodesic-synchrotron-radiation (GSR) spectra are determined for the case of a test particle moving on a highly relativistic circular orbit about a rotating (Kerr) black hole. It is found that the spectral shape depends only weakly on the value of the angular-momentum parameter (a/M) of the black hole, but the total radiated power drops unexpectedly for a value of at least 0.95 and vanishes as the value approaches unity. A spin-dependent factor (involving the inner product of the polarization of a radiated quantum with the source) is isolated to explain the dependence of the spectral shape on the spin of the radiated field. Although the scalar wave equation is solved by separation of variables, this procedure is avoided for the vector and tensor cases by postulating a sum-over-states expansion for the Green's function similar to that found to hold in the scalar case. The terms in this sum, significant for GSR, can then be evaluated in the geometric-optics approximation without requiring the use of vector or tensor spherical harmonics.

Chrzanowski, P. L.↗
NASA NTRS1976

A study of sound transmission in curved duct bends by the Galerkin method

A computational procedure based on the Galerkin method is developed to study the sound transmission and reflection characteristics of circularly curved bends of rectangular ducts. This procedure is adaptable to routine computer calculation. An important component of the computer program consists of a QR iterative algorithm which solves the matrix eigenvalue problem generated by the Galerkin method. The present procedure produced very satisfactory convergent results when applied even to cases where the incident wave has high frequency and high wave mode numbers. Some properties of the Galerkin solution are investigated. Its relationship to the classical solution by the method of separation of variables is discussed.

Tam, C. K. W.↗
NASA NTRS1976

The theory of the gravitational potential applied to orbit prediction

A complete derivation of the geopotential function and its gradient is presented. Also included is the transformation of Laplace's equation from Cartesian to spherical coordinates. The analytic solution to Laplace's equation is obtained from the transformed version, in the classical manner of separating the variables. A cursory introduction to the method devised by Pines, using direction cosines to express the orientation of a point in space, is presented together with sample computer program listings for computing the geopotential function and the components of its gradient. The use of the geopotential function is illustrated.

Kirkpatrick, J. C.↗
NASA NTRS1976

Parameters affecting electrostatic cooling

A high voltage electrostatic field is discussed which enhances the rate of normal convective cooling. This cooling rate is a function of starting temperature and voltage applied, and an inverse function of atmospheric pressure or the heat capacity of the surrounding media. It appears that the cooling rate is also a function of current flow; however, additional work is needed to separate other variables from the effect of current flow. The maximum increase in heat loss over the normal convective cooling was approximately 0.167 C/sec (0.3 F/sec) at 316 C (600 F) and 20,000 V. From the data taken it is assumed that the addeded rate of cooling would be increased with higher temperatures and higher voltages. It appears that a high voltage field disrupts the molecular layer of air surrounding a hot body and increases the rate of convective cooling.

Demorest, K. E.↗
NASA NTRS1977

Summer performance results obtained from simultaneously testing ten solar collectors outdoors

Ten solar collectors were simultaneously tested outdoors. Efficiency data were correlated using a method that separates solar variables (flux, incident angle) from the desired performance parameters (heat loss, absorbtance, transmittance) which are unique to a given collector design. Tests were conducted on both clear and moderately cloudy days. Correlating data in the above manner, a 2-glass, black paint collector exhibited a decrease in efficiency of 5 percentage points relative to the baseline data for an exposure time of 2 years, 4 months. Condensation on the collector glazing was thought to be a contributing factor in this efficiency change.

Miller, D. R.↗
NASA NTRS1979

Spectral methods for problems in complex geometries

Techniques that permit the efficient application of spectral methods to solve problems in nearly arbitrary geometries are presented. These methods were found to be viable alternatives to finite difference and finite element processes. The spectral methods applied are extensions of the standard techniques of separation of variables to the solution of arbitrarily complicated problems.

Orszag, S. A.↗
NASA NTRS1983

Interpretation of 2-probe turbulence measurements in an axisymmetric contraction

Simultaneous measurements of the streamwise and radial velocity components at two points, one on and one off the centerline with variable radial separation, were digitally recorded and processed at several stations along a four to one contraction with controlled upstream turbulence conditions. Various statistical quantities are presented including spectra and coherence functions. The integral L sub ux, L sub um, L sub vx, L sub vm were also estimated and their variation along the contraction is examined.

Marion-Moulin, C.↗
NASA NTRS1982

Solution to the backward-Kolmogorov equation for a nonstationary oscillation problem

The transition probability density function of a Markovian approximation of the response amplitude of an oscillator under nonstationary excitation is determined in an analytical form. A solution is presented for the associated backward-Kolmogorov equation by transforming the equation into a form amenable to solution by the method of the separation of variables. This procedure results in a boundary value problem which is then solved by using an infinite series of Laguerre polynomials. It is found that the infinite series solution is equivalent to a closed-form solution involving a Bessel function.

Solomos, G. P.↗