Analytic model for describing the operation of the Marzolf tunnel diode inverter.
Analytic model for describing operation of Marzolf tunnel diode inverter
INVERTER↗
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Results for “Analytical mathematics”
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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Thermal testing techniques at high solar intensities.
Thermal testing techniques for solar probe spacecraft using analytical and experimental models
SOLAR PROBE↗
Applications of a quadratic extended interior penalty function for structural optimization
A quadratic extended interior penalty function formulation especially well suited for second-order unconstrained optimization procedures is presented. Analytical derivatives of constraints and an approximate analysis technique are used. Minimum-mass design results are presented which indicate that the combination of these procedures can help make mathematical programming a useful optimization tool for large-order structural design problems with a large number of design variables and multiple constraints. Examples include statically loaded high- and low-aspect-ratio wings simultaneously subjected to stress, displacement, minimum gage and, in some cases, maximum strain constraints.
Haftka, R. T.↗
Two-dimensional turbulence in inviscid fluids or guiding center plasmas
Numerical tests of the inviscid equilibrium theory of Kraichnan (1975) are described. The mathematical description applies equally well to the two-dimensional electrostatic guiding center plasma and to the two-dimensional inviscid Navier-Stokes fluid. The predictions of this analytic theory are discussed. A pair of coupled equations are derived for the two-time vorticity autocorrelation in Fourier space and the infinitesimal unit response function G of Kraichnan in the so-called Eulerian direct interaction approximation. Kraichnan's assertion that thermodynamic limits exist for the negative temperature states is questioned.
Seyler, C. E., Jr.↗
A theoretical investigation of noise reduction through the cylindrical fuselage of a twin-engine, propeller-driven aircraft
Interior noise in the fuselage of a twin-engine, propeller-driven aircraft with two propellers rotating in opposite directions is studied analytically. The fuselage was modeled as a stiffened cylindrical shell with simply supported ends, and the effects of stringers and frames were averaged over the shell surface. An approximate mathematical model of the propeller noise excitation was formulated which includes some of the propeller noise characteristics such as sweeping pressure waves around the sidewalls due to propeller rotation and the localized nature of the excitation with the highest levels near the propeller plane. Results are presented in the form of noise reduction, which is the difference between the levels of external and interior noise. The influence of propeller noise characteristics on the noise reduction was studied. The results indicate that the sweep velocity of the excitation around the fuselage sidewalls is critical to noise reduction.
Bhat, R. B.↗
Dynamics of A Vibration Isolation System Including Inertia of the Human Body
Using an exercise device in a spacecraft is liable to transmit an unacceptable amount of vibration to that vehicle. This is commonly mitigated by a Vibration Isolation System (VIS), whose dynamics must be analyzed to confirm that the oscillatory forces on the spacecraft remain within allowed range, both from a structural and microgravity perspective (see, e.g., [1]). When modeling a VIS for countermeasures devices, one common approach is to record forces and moments applied on the floor while exercising, and then drive the VIS simulation by applying these recorded loads to the exercise platform part of the VIS mechanical model. This approach misses the fact that when exercising on a moving platform, the force and moment on it will differ from that on the stationary floor due to inertial effects involving the human body. For example, standing up on a platform as it gives under the subject’s feet reduces the foot force on it, and such inertial effects are especially complex for rotational motion. In principle, one could model both the motion of the human body and dynamics of the VIS mechanism in a single combined simulation, e.g., employing a tool such as the commonly used biomechanical simulation OpenSim. Here, the joints of the human body would be driven kinematically along prescribed exercise trajectories while the dynamics engine computed the response of the VIS degrees of freedom. However, mechanism designers and biomechanics experts have their own established tools, making it very desirable to have a way of decoupling the biomechanics from the VIS modeling, simulation, and analyses. We have derived a set of equations that rigorously accomplishes this goal, and have implemented them as an interface function that provides an alternative driving mechanism for an existing force-based VIS analysis simulation. When enabled, the simulated human/VIS system dynamics is now driven by this function, instead of the recorded force methodology described above. The function is designed to accept input from a data file containing the required time-stamped human motion and inertia terms corresponding to the specific exercise in question. This data file is generated by an OpenSim plugin written for that purpose. The existing VIS analytical simulation is developed using NASA’s Trick Simulation Environment [2], as well as its MBDyn multibody dynamics [3] package. The presentation will provide a detailed overview of the mathematical formulation, assumptions, plugin implementation, software interfaces, and results for a sample set of representative exercises. The results from this work aim to better inform VIS design efforts, as well as countermeasure device/protocol designs with respect to exercise type and frequency effects on vehicle structural and microgravity restrictions.
Countermeasures↗
The Thin Oil Film Equation
A thin film of oil on a surface responds primarily to the wall shear stress generated on that surface by a three-dimensional flow. The oil film is also subject to wall pressure gradients, surface tension effects and gravity. The partial differential equation governing the oil film flow is shown to be related to Burgers' equation. Analytical and numerical methods for solving the thin oil film equation are presented. A direct numerical solver is developed where the wall shear stress variation on the surface is known and which solves for the oil film thickness spatial and time variation on the surface. An inverse numerical solver is also developed where the oil film thickness spatial variation over the surface at two discrete times is known and which solves for the wall shear stress variation over the test surface. A One-Time-Level inverse solver is also demonstrated. The inverse numerical solver provides a mathematically rigorous basis for an improved form of a wall shear stress instrument suitable for application to complex three-dimensional flows. To demonstrate the complexity of flows for which these oil film methods are now suitable, extensive examination is accomplished for these analytical and numerical methods as applied to a thin oil film in the vicinity of a three-dimensional saddle of separation.
Brown, James L.↗
Small rocket exhaust plume data
During recent cryodeposit tests with an 0.18-N thruster, the mass flux in the plume back field was measured for the first time for nitrogen, carbon dioxide, and a mixture of nitrogen, hydrogen, and ammonia at various inlet pressures. This mixture simulated gases that would be generated by a hydrazine plenum attitude propulsion system. The measurements furnish a base upon which to build a mathematical model of plume back flow that will be used in predicting the mass distribution in the boundary region of other plumes. The results are analyzed and compared with existing analytical predictions.
Chirivella, J. E.↗
Visible-infrared remote-sensing model and applications for ocean waters
Remote sensing has become important in the ocean sciences, especially for research involving large spatial scales. To estimate the in-water constituents through remote sensing, whether carried out by satellite or airplane, the signal emitted from beneath the sea surface, the so called water-leaving radiance (L(w)), is of prime importance. The magnitude of L(w) depends on two terms: one is the intensity of the solar input, and the other is the reflectance of the in-water constituents. The ratio of the water-leaving radiance to the downwelling irradiance (E(d)) above the sear surface (remote-sensing reflectance, R(sub rs)) is independent of the intensity of the irradiance input, and is largely a function of the optical properties of the in-water constituents. In this work, a model is developed to interpret r(sub rs) for ocean water in the visible-infrared range. In addition to terms for the radiance scattered from molecules and particles, the model includes terms that describe contributions from bottom reflectance, fluorescence of gelbstoff or colored dissolved organic matter (CDOM), and water Raman scattering. By using this model, the measured R(sub rs) of waters from the West Florida Shelf to the Mississippi River plume, which covered a (concentration of chlorophyll a) range of 0.07 - 50 mg/cu m, were well interpreted. The average percentage difference (a.p.d.) between the measured and modeled R(sub rs) is 3.4%, and, for the shallow waters, the model-required water depth is within 10% of the chart depth. Simple mathematical simulations for the phytoplankton pigment absorption coefficient (a(sub theta)) are suggested for using the R(sub rs) model. The inverse problem of R(sub rs), which is to analytically derive the in-water constituents from R(sub rs) data alone, can be solved using the a(sub theta) functions without prior knowledge of the in-water optical properties. More importantly, this method avoids problems associated with a need for knowledge of the shape and value of the chlorophyll-specific absorption coefficient. The simulation was tested for a wide range of water types, including waters from Monterey Bay, the West Florida Shelf, and the Mississippi River plume. Using the simulation, the R(sub rs)-derived in-water absorption coefficients were consistent with the values from in-water measurements (r(exp 2) greater than 0.94, slope approximately 1.0). In the remote-sensing applications, a new approach is suggested for the estimation of primary production based on remote sensing. Using this approach, the calculated primary production (PP) values based upon remotely sensed data were very close to the measured values for the euphotic zone (r(exp 2) = 0.95, slope 1.26, and 32% average difference), while traditional, pigment-based PP model provided values only one-third the size of the measured data. This indicates a potential to significantly improve the accuracy of the estimation of primary production based upon remote sensing.
Lee, Zhongping↗
Pulse Phase Thermography for Defect Detection and Visualization
Pulse Phase Thermography (PPT) has been reported as a novel powerful technique of the thermal NDE. It employs application of the Discrete Fourier Transform (DFT) to thermal images obtained following flash heating of the front surface of a specimen. The computed phasegrams are excellent for defect visualization in a wide range of materials. This is in part due to their low sensitivity to uneven heating. This work is an attempt to analyze advantages and limitations of PPT. Results of application of the DFT to simulated temperature decays are presented. The temperature evolution on a surface has been simulated based on an analytical solution of the one-dimensional heat diffusion problem. A more sophisticated study has been done for different sizes of defects using numerical solution of the three-dimensional mathematical model. Capabilities of PPT for in-depth scanning and for monitoring of the material loss are discussed. The recommendations for the practical application of the PPT are presented. Experimental results obtained following these recommendations are reported.
Marinetti, Sergio↗
Analytical and experimental studies of an optimum multisegment phased liner noise suppression concept
Results are presented from detailed analytical studies made to define methods for obtaining improved multisegment lining performance by taking advantage of relative placement of each lining segment. Properly phased liner segments reflect and spatially redistribute the incident acoustic energy and thus provide additional attenuation. A mathematical model was developed for rectangular ducts with uniform mean flow. Segmented acoustic fields were represented by duct eigenfunction expansions, and mode-matching was used to ensure continuity of the total field. Parametric studies were performed to identify attenuation mechanisms and define preliminary liner configurations. An optimization procedure was used to determine optimum liner impedance values for a given total lining length, Mach number, and incident modal distribution. Optimal segmented liners are presented and it is shown that, provided the sound source is well-defined and flow environment is known, conventional infinite duct optimum attenuation rates can be improved. To confirm these results, an experimental program was conducted in a laboratory test facility. The measured data are presented in the form of analytical-experimental correlations. Excellent agreement between theory and experiment verifies and substantiates the analytical prediction techniques. The results indicate that phased liners may be of immediate benefit in the development of improved aircraft exhaust duct noise suppressors.
Sawdy, D. T.↗
Tests characterizing bioprocessor hardware for analytical modeling
The tests outlined in this paper were used to characterize the hardware components of the Salad Machine, a small NASA-developed bioprocessor. The data from these tests are presented, and the methods by which this data can be integrated into system mathematical models are briefly discussed. The subsystems and physical processes discussed include the lighting system, the air loop (condensing heat exchanger and the blower), heat transfer to the surroundings, and leakage. Through this effort it was learned that in the development of a test protocol, care should be taken to order the tests such that environmental parameters, particularly humidity, require as few large adjustments as possible. Sensor calibration and installation take a substantial amount of time, which should be built into the test schedule. Two properties were particularly hard to quantify: the air flow rate and the energy from the lighting system entering into the growth volume. Flow rate can be measured using the appropriate device for the system configuration and airflow. Lighting system radiation level was measured using three methods. The results of these methods varied substantially, putting off conclusive quantification of this value.
Gustavino, S.↗
Computer prediction of large reflector antenna radiation properties
A FORTRAN program for calculating reflector antenna radiation patterns was rewritten and extended to include reflectors composed of a number of panels. These individual panels must be analytic surfaces. The theoretical foundation for the program is as follows: Geometrical optics techniques are used to trace rays from a feed antenna to the reflector surface and back to a mathematical plane just in front of the reflector. The resulting tangential electric field distribution, assumed to be the only source of forward radiation, is integrated numerically to calculate the radiation pattern for a desired set of angles. When the reflector is composed of more than one panel, each panel is treated as a separated antenna, the ray-tracing procedure and integration being repeated for each panel. The results of the individual aperture plane integrations are stored and summed to yield the relative electric field strength over the angles of interest. An example and several test cases are included to demonstrate the use of the program and verify the new method of computation.
Botula, A.↗
Statistical methods for astronomical data with upper limits. I - Univariate distributions
The statistical treatment of univariate censored data is discussed. A heuristic derivation of the Kaplan-Meier maximum-likelihood estimator from first principles is presented which results in an expression amenable to analytic error analysis. Methods for comparing two or more censored samples are given along with simple computational examples, stressing the fact that most astronomical problems involve upper limits while the standard mathematical methods require lower limits. The application of univariate survival analysis to six data sets in the recent astrophysical literature is described, and various aspects of the use of survival analysis in astronomy, such as the limitations of various two-sample tests and the role of parametric modelling, are discussed.
Feigelson, E. D.↗
Expressions Module for the Satellite Orbit Analysis Program
The Expressions Module is a software module that has been incorporated into the Satellite Orbit Analysis Program (SOAP). The module includes an expressions- parser submodule built on top of an analytical system, enabling the user to define logical and numerical variables and constants. The variables can capture output from SOAP orbital-prediction and geometric-engine computations. The module can combine variables and constants with built-in logical operators (such as Boolean AND, OR, and NOT), relational operators (such as >, <, or =), and mathematical operators (such as addition, subtraction, multiplication, division, modulus, exponentiation, differentiation, and integration). Parentheses can be used to specify precedence of operations. The module contains a library of mathematical functions and operations, including logarithms, trigonometric functions, Bessel functions, minimum/ maximum operations, and floating- point-to-integer conversions. The module supports combinations of time, distance, and angular units and has a dimensional- analysis component that checks for correct usage of units. A parser based on the Flex language and the Bison program looks for and indicates errors in syntax. SOAP expressions can be built using other expressions as arguments, thus enabling the user to build analytical trees. A graphical user interface facilitates use.
Edmonds, Karina↗
Gas bearings
The present work deals with the fundamentals of gas lubrication theory, which forms the foundation of all analytical design tools for gas bearings. Most of the hard lessons learned in the past are outlined with reference to dry contact, debris ingestion, sliding speed, and chemical stability of lubricant. The mathematical theory of gas lubrication is described for scaling rules in thin-film viscous flow, momentum conservation, mass conservation, energy conservation, isothermal gas bearing theory, coupling effects, and global bearing characteristics. Particular attention is given to the governing differential equations for common bearing configurations. Also discussed are representative solutions of self-acting gas bearings, externally pressurized bearings, and time-dependent effects.
Pan, C. H. T.↗
Optimal searches for asteroids
Optimal searches for a fixed object are discussed, and the rigorous analytical results of discrete search theory are presented. The totally optimal, the uniformly optimal, the locally optimal, and the fastest searches are shown to be identical under not too restrictive assumptions. The mathematical formalism is illustrated by an Earth-approaching asteroid search and optimal searches for such objects are explicitly constructed. The approximation that Earth-approaching asteroids are fixed is equivalent to having a very high ( equiv 100 sq degs/hour) search rate. Generalizations to other types of astronomical search are briefly mentioned.
Taff, L. G.↗
Optimal searches for asteroids
Optimal searches for a fixed object are discussed, and the rigorous analytical results of discrete search theory are presented. The totally optimal, the uniformly optimal, the locally optimal, and the fastest searches are shown to be identical under not too restrictive assumptions. The mathematical formalism is illustrated by an earth-approaching asteroid search and optimal searches for such objects are explicitly constructed. The approximation that earth-approaching asteroids are fixed is equivalent to having a very high (equiv 100 sq degs/hour) search rate. Generalizations to other types of astronomical search are briefly mentioned. Previously announced in STAR as N83-34657
Taff, L. G.↗