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NASA NTRS1993

A modified Chebyshev pseudospectral method with an O(N exp -1) time step restriction

The extreme eigenvalues of the Chebyshev pseudospectral differentiation operator are O(N exp 2) where N is the number of grid points. As a result of this, the allowable time step in an explicit time marching algorithm is O(N exp -2) which, in many cases, is much below the time step dictated by the physics of the partial differential equation. A new set of interpolating points is introduced such that the eigenvalues of the differentiation operator are O(N) and the allowable time step is O(N exp -1). The properties of the new algorithm are similar to those of the Fourier method. The new algorithm also provides a highly accurate solution for non-periodic boundary value problems.

Kosloff, Dan↗

NASA NTRS1973

PLZT block data composers operated in differential phase mode

The use of a PLTZ block data composer as a matrix type phase modulator to record and process digital data by the differential phase mode in a holographic recording/processing system was investigated. The system has readout contrast ratios of between 10 and 15 to 1. The differential phase mode has the advantage that strain bias is not required and thickness and strain variations in the PLZT are cancelled out.

Drake, M. D.↗

NASA NTRSDate not supplied

Thermal Vacuum and Vibration Testing of the Differential Thermal Expansion Thermal Switch

The Extended Stroke, Reverse Operation, Differential Expansion Thermal Switch for Extreme Variable Environments uses materials with both positive and negative coefficients of thermal expansion (CTE) arranged in concentric cylinders so that the thermal switch (TS) operates passively, opening a gap between interfaces to create a low thermal contact when cold, and closing the gap between interfaces to create a high thermal contact when hot. This paper details the testing of the TS at Marshall Space Flight Center including the pre-vibe thermal vacuum cycle test, vibration test, post-vibe thermal vacuum cycle test, and long duration thermal vacuum cycle test. The pre- and post-vibe thermal cycle and the long duration cycle test tested to hot and cold plateau initial temperatures of 40 °C, and -173 °C, respectively. The pre- and post-vibe tests required plateau holds of at least 2 hours, whereas the long duration cycle test required plateau holds of at least 20 hours. The tests each used a rate of temperature change of < 2 °C/min when transitioning between plateaus. The data collected from each thermal test is compared to show the operation of the TS both before and after the vibration test to GEVS levels, and throughout the long duration cycle test. From the data collected, the total conductance through the TS interfaces is calculated for both on (TS closed – during hot plateau) and off (TS open – during cold plateau) configurations, and the turndown ratio is also calculated. Challenges and lessons learned from the testing are also discussed.

thermal control technology↗

NASA NTRS2023

Thermal Vacuum and Vibration Testing of the Differential Thermal Expansion Thermal Switch

The Extended Stroke, Reverse Operation, Differential Thermal Expansion (DTE) Thermal Switch (TS) for Extreme Variable Environments uses materials with both positive and negative coefficients of thermal expansion (CTE) arranged in concentric cylinders so that the TS operates passively, opening a gap between interfaces to create a low thermal contact when cold, and closing the gap between interfaces to create a high thermal contact when hot. This paper details the testing of the TS at Marshall Space Flight Center (MSFC) including the vibration (vibe) test, pre-vibe thermal vacuum (t-vac) cycle test, post-vibe t-vac cycle test, and long duration t-vac cycle test. The data collected from the pre- and post-vibe tests are compared to show the impact of the vibe test on performance. The data collected from the long duration test is used to calculate the total thermal contact conductance through the TS interfaces for both ‘on’ (TS closed, during hot plateau) and ‘off’ (TS open, during cold plateau) configurations, and the turndown ratio is also calculated. Challenges experienced throughout testing are also discussed.

Thermal control technology↗

NASA NTRS2023

Thermal Vacuum and Vibration Testing of the Differential Thermal Expansion Thermal Switch

Thermal control technology↗

NASA NTRS1990

Worldwide differential GPS for Space Shuttle landing operations

Worldwide differential Global Positioning System (WWDGPS) is viewed as an effective method of offering continuous high-quality navigation worldwide. The concept utilizes a network with as few as 33 ground stations to observe most of the error sources of GPS and provide error corrections to users on a worldwide basis. The WWDGPS real-time GPS tracking concept promises a threefold or fourfold improvement in accuracy for authorized dual-frequency users, and in addition maintains an accurate and current ionosphere model for single-frequency users. A real-time global tracking network also has the potential to reverse declarations of poor health on marginal satellites, increasing the number of satellites in the constellation and lessening the probability of GPS navigation outage. For Space Shuttle operations, the use of WWDGPS-aided P-code equipment promises performance equal to or better than other current landing guidance systems in terms of accuracy and reliability. This performance comes at significantly less cost to NASA, which will participate as a customer in a system designed as a commercial operation serving the global civil navigation community.

Loomis, Peter V. W.↗

NASA NTRS1994

On the convergence of local approximations to pseudodifferential operators with applications

We consider the approximation of a class pseudodifferential operators by sequences of operators which can be expressed as compositions of differential operators and their inverses. We show that the error in such approximations can be bounded in terms of L(1) error in approximating a convolution kernel, and use this fact to develop convergence results. Our main result is a finite time convergence analysis of the Engquist-Majda Pade approximants to the square root of the d'Alembertian. We also show that no spatially local approximation to this operator can be convergent uniformly in time. We propose some temporally local but spatially nonlocal operators with better long time behavior. These are based on Laguerre and exponential series.

Hagstrom, Thomas↗

NASA NTRS2010

Special Component Designs for Differential-Amplifier MMICs

Special designs of two types of electronic components transistors and transmission lines have been conceived to optimize the performances of these components as parts of waveguide-embedded differential-amplifier monolithic microwave integrated circuits (MMICs) of the type described in the immediately preceding article. These designs address the following two issues, the combination of which is unique to these particular MMICs: Each MMIC includes a differential double-strip transmission line that typically has an impedance between 60 and 100 W. However, for purposes of matching of impedances, transmission lines having lower impedances are also needed. The transistors in each MMIC are, more specifically, one or more pair(s) of InP-based high-electron-mobility transistors (HEMTs). Heretofore, it has been common practice to fabricate each such pair as a single device configured in the side-to-side electrode sequence source/gate/drain/gate/source. This configuration enables low-inductance source grounding from the sides of the device. However, this configuration is not suitable for differential operation, in which it is necessary to drive the gates differentially and to feed the output from the drain electrodes differentially. The special transmission-line design provides for three conductors, instead of two, in places where lower impedance is needed. The third conductor is a metal strip placed underneath the differential double-strip transmission line. The third conductor increases the capacitance per unit length of the transmission line by such an amount as to reduce the impedance to between 5 and 15 W. In the special HEMT-pair design, the side-to-side electrode sequence is changed to drain/gate/source/gate/ drain. In addition, the size of the source is reduced significantly, relative to corresponding sizes in prior designs. This reduction is justified by the fact that, by virtue of the differential configuration, the device has an internal virtual ground, and therefore there is no need for a low-resistance contact between the source and the radio-frequency circuitry. The source contact is needed only for DC biasing. These designs were implemented in a single-stage-amplifier MMIC. In a test at a frequency of 305 GHz, the amplifier embedded in a waveguide exhibited a gain of 0 dB; after correcting for the loss in the waveguide, the amplifier was found to afford a gain of 0.9 dB. In a test at 220 GHz, the overall gain of the amplifier- and-waveguide assembly was found to be 3.5 dB.

Kangaslahti, Pekka↗

NASA NTRS1983

Simulation and analysis of differential global positioning system for civil helicopter operations

A Differential Global Positioning System (DGPS) computer simulation was developed, to provide a versatile tool for assessing DGPS referenced civil helicopter navigation. The civil helicopter community will probably be an early user of the GPS capability because of the unique mission requirements which include offshore exploration and low altitude transport into remote areas not currently served by ground based Navaids. The Monte Carlo simulation provided a sufficiently high fidelity dynamic motion and propagation environment to enable accurate comparisons of alternative differential GPS implementations and navigation filter tradeoffs. The analyst has provided the capability to adjust most aspects of the system, the helicopter flight profile, the receiver Kalman filter, and the signal propagation environment to assess differential GPS performance and parameter sensitivities. Preliminary analysis was conducted to evaluate alternative implementations of the differential navigation algorithm in both the position and measurement domain. Results are presented to show that significant performance gains are achieved when compared with conventional GPS but that differences due to DGPS implementation techniques were small. System performance was relatively insensitive to the update rates of the error correction information.

Denaro, R. P.↗

NASA NTRS1989

Absorbing boundary conditions for second-order hyperbolic equations

A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.

Jiang, Hong↗

NASA NTRS1990

Absorbing boundary conditions for second-order hyperbolic equations

Jiang, Hong↗

NASA NTRS1972

Reflecting Solutions of High Order Elliptic Differential Equations in Two Independent Variables Across Analytic Arcs

Consideration is given specifically to sixth order elliptic partial differential equations in two independent real variables x, y such that the coefficients of the highest order terms are real constants. It is assumed that the differential operator has distinct characteristics and that it can be factored as a product of second order operators. By analytically continuing into the complex domain and using the complex characteristic coordinates of the differential equation, it is shown that its solutions, u, may be reflected across analytic arcs on which u satisfies certain analytic boundary conditions. Moreover, a method is given whereby one can determine a region into which the solution is extensible. It is seen that this region of reflection is dependent on the original domain of difinition of the solution, the arc and the coefficients of the highest order terms of the equation and not on any sufficiently small quantities; i.e., the reflection is global in nature. The method employed may be applied to similar differential equations of order 2n.

Carleton, O.↗

NASA NTRS2001

On the Definition of Surface Potentials for Finite-Difference Operators

For a class of linear constant-coefficient finite-difference operators of the second order, we introduce the concepts similar to those of conventional single- and double-layer potentials for differential operators. The discrete potentials are defined completely independently of any notion related to the approximation of the continuous potentials on the grid. We rather use all approach based on differentiating, and then inverting the differentiation of a function with surface discontinuity of a particular kind, which is the most general way of introducing surface potentials in the theory of distributions. The resulting finite-difference "surface" potentials appear to be solutions of the corresponding continuous potentials. Primarily, this pertains to the possibility of representing a given solution to the homogeneous equation on the domain as a variety of surface potentials, with the density defined on the domain's boundary. At the same time the discrete surface potentials can be interpreted as one specific realization of the generalized potentials of Calderon's type, and consequently, their approximation properties can be studied independently in the framework of the difference potentials method by Ryaben'kii. The motivation for introducing and analyzing the discrete surface potentials was provided by the problems of active shielding and control of sound, in which the aforementioned source terms that drive the potentials are interpreted as the acoustic control sources that cancel out the unwanted noise on a predetermined region of interest.

Tsynkov, S. V.↗

NASA NTRS1984

Application of differential GPS to civil helicopter terminal guidance

NASA is conducting a research program to evaluate differential Global Positioning System (GPS) concepts for civil helicopter navigation. It is pointed out that the civil helicopter community will probably be an early user of GPS because of the unique mission operations in areas where precise navigation aids are not available. Applications with very demanding accuracy requirements are related to remote area search and rescue, offshore oil platform approach, remote area precision landing, and other precise navigation operations. Differential GPS appears to provide a solution for meeting the accuracy requirements involved in the considered operations. The present investigation is concerned with results obtained in three areas studied in connection with the conducted research program. Attention is given to mission-tailored satellite selection, a satellite selection algorithm concept, satellite selection algorithm simulation results, and differential GPS ground station design.

Denaro, R. P.↗

NASA NTRS1992

A comparison of artificial compressibility and fractional step methods for incompressible flow computations

We have applied and compared the efficiency and accuracy of two commonly used numerical methods for the solution of Navier-Stokes equations. The artificial compressibility method augments the continuity equation with a transient pressure term and allows one to solve the modified equations as a coupled system. Due to its implicit nature, one can have the luxury of taking a large temporal integration step at the expense of higher memory requirement and larger operation counts per step. Meanwhile, the fractional step method splits the Navier-Stokes equations into a sequence of differential operators and integrates them in multiple steps. The memory requirement and operation count per time step are low, however, the restriction on the size of time marching step is more severe. To explore the strengths and weaknesses of these two methods, we used them for the computation of a two-dimensional driven cavity flow with Reynolds number of 100 and 1000, respectively. Three grid sizes, 41 x 41, 81 x 81, and 161 x 161 were used. The computations were considered after the L2-norm of the change of the dependent variables in two consecutive time steps has fallen below 10(exp -5).

Chan, Daniel C.↗

NASA NTRS1995

On the nonlinear stability of the unsteady, viscous flow of an incompressible fluid in a curved pipe

The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.

Shortis, Trudi A.↗

NASA NTRS1969

Integral valve provides automatic relief and remote venting

In-line, pilot-operated, differential area, poppet type valve provides both automatic relief of a tank at a precise over-pressure and remote control of tank venting. Relief and vent operations are separate functions incorporated in an integral valve package.

Gilmore, R. F.↗

NASA NTRS1985

Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies

Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are useed to argue convergence and establish rates of convergence. An example and numerical results are discussed.

Rosen, I. G.↗