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NASA NTRS1984

Advanced numerics for multi-dimensional fluid flow calculations

In recent years, there has been a growing interest in the development and use of mathematical models for the simulation of fluid flow, heat transfer and combustion processes in engineering equipment. The equations representing the multi-dimensional transport of mass, momenta and species are numerically solved by finite-difference or finite-element techniques. However despite the multiude of differencing schemes and solution algorithms, and the advancement of computing power, the calculation of multi-dimensional flows, especially three-dimensional flows, remains a mammoth task. The following discussion is concerned with the author's recent work on the construction of accurate discretization schemes for the partial derivatives, and the efficient solution of the set of nonlinear algebraic equations resulting after discretization. The present work has been jointly supported by the Ramjet Engine Division of the Wright Patterson Air Force Base, Ohio, and the NASA Lewis Research Center.

Vanka, S. P.↗

NASA NTRS2009

Application of TRMM PR and TMI Measurements to Assess Cloud Microphysical Schemes in the MM5 Model for a Winter Storm

Seen by the human eye, precipitation particles are commonly drops of rain, flakes of snow, or lumps of hail that reach the ground. Remote sensors and numerical models usually deal with information about large collections of rain, snow, and hail (or graupel --also called soft hail ) in a volume of air. Therefore, the size and number of the precipitation particles and how particles interact, evolve, and fall within the volume of air need to be represented using physical laws and mathematical tools, which are often implemented as cloud and precipitation microphysical parameterizations in numerical models. To account for the complexity of the precipitation physical processes, scientists have developed various types of such schemes in models. The accuracy of numerical weather forecasting may vary dramatically when different types of these schemes are employed. Therefore, systematic evaluations of cloud and precipitation schemes are of great importance for improvement of weather forecasts. This study is one such endeavor; it pursues quantitative assessment of all the available cloud and precipitation microphysical schemes in a weather model (MM5) through comparison with the observations obtained by National Aeronautics and Space Administration (NASA) s and Japan Aerospace Exploration Agency (JAXA) s Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) and microwave imager (TMI). When satellite sensors (like PR or TMI) detect information from precipitation particles, they cannot directly observe the microphysical quantities (e.g., water species phase, density, size, and amount etc.). Instead, they tell how much radiation is absorbed by rain, reflected away from the sensor by snow or graupel, or reflected back to the satellite. On the other hand, the microphysical quantities in the model are usually well represented in microphysical schemes and can be converted to radiative properties that can be directly compared to the corresponding PR and TMI observations. This study employs this method to evaluate the accuracy of the simulated radiative properties by the MM5 model with different microphysical schemes. It is found that the representations of particle density, size, and mass in the different schemes in the MM5 model determine the model s performance when predicting a winter storm over the eastern Pacific Ocean. Schemes lacking moderate density particles (i.e. graupel), with snow flakes that are too large, or with excessive mass of snow or graupel lead to degraded prediction of the radiative properties as observed by the TRMM satellite. This study demonstrates the uniqueness of the combination of both an active microwave sensor (PR) and passive microwave sensor (TMI) onboard TRMM on assessing the accuracy of numerical weather forecasting. It improves our understanding of the physical and radiative properties of different types of precipitation particles and provides suggestions for better representation of cloud and precipitation processes in numerical models. It would, ultimately, contribute to answering questions like "Why did it not rain when the forecast says it would?"

Han, Mei↗

NASA NTRS1967

CINDA - Chrysler Improved Numerical Differencing Analyzer computer program

Dimensionless multioption systems compiler computer program constructs and analyzes a mathematical model of any arbitrary one, two, or three dimensional lumped parameter representation of a physical system. It automatically optimizes the utilization of computer core space and is more general and versatile than BETA.

Gaski, J. D.↗

NASA NTRS1993

Sloshing dynamics on rotating helium dewar tank

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by both the gravity gradient and jitter accelerations applicable to scientific spacecraft which is eligible to carry out spinning motion and/or slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with Gravity Probe-B (GP-B) spacecraft which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics were based on the non-inertia frame spacecraft bound coordinate, and solve time dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers were derived. Results were widely published in the open journals.

Hung, R. J.↗

NASA NTRS1994

Superfluid helium sloshing dynamics induced oscillations and fluctuations of angular momentum, force and moment actuated on spacecraft driven by gravity gradient or jitter acceleration associated with slew motion

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by the gravity gradient and jitter accelerations associated with slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) for slew motion which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics is based on the non-inertia frame spacecraft bound coordinate, and solve time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid-vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers have also been derived. Examples are also given for cases applicable to the AXAF-S spacecraft sloshing dynamics associated with slew motion.

Hung, R. J.↗

NASA NTRS1986

Optimization methods and silicon solar cell numerical models

The goal of this project is the development of an optimization algorithm for use with a solar cell model. It is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junctions depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm has been developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAPID). SCAPID uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the operation of a solar cell. A major obstacle is that the numerical methods used in SCAPID require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the value associated with the maximum efficiency. This problem has been alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution. Adapting SCAPID so that it could be called iteratively by the optimization code provided another means of reducing the cpu time required to complete an optimization. Instead of calculating the entire I-V curve, as is usually done in SCAPID, only the efficiency is calculated (maximum power voltage and current) and the solution from previous calculations is used to initiate the next solution.

Girardini, K.↗

NASA NTRS1985

The method of complex characteristics for transonic airfoil design, with an application to compressors

The use of mathematical models to study physical problems of current interest to aeronautical engineers has been made possible by the development of numerical techniques to compute solutions of the differential equations of transonic aerodynamics. These advances have encouraged the improvement of supercritical wing technology. A method to determined steady, shockless flow of an inviscid, compressible fluid past a cascade of airfoils in the (x,y)-plane is considered, taking into account also the case of an isolated airfoil. The method of complex characteristics solves the equations in the hodograph plane by extending all variables into the complex domain, where the notion of type is no longer significant. Attention is given to the mathematical background, the method of complex characteristics, and numerical calculations.

Bledsoe, M.↗

NASA NTRS1980

Handling qualities of large flexible control-configured aircraft

The effects on handling qualities of low frequency symmetric elastic mode interaction with the rigid body dynamics of a large flexible aircraft was analyzed by use of a mathematical pilot modeling computer simulation. An extension of the optimal control model for a human pilot was made so that the mode interaction effects on the pilot's control task could be assessed. Pilot ratings were determined for a longitudinal tracking task with parametric variations in the undamped natural frequencies of the two lowest frequency symmetric elastic modes made to induce varying amounts of mode interaction. Relating numerical performance index values associated with the frequency variations used in several dynamic cases, to a numerical Cooper-Harper pilot rating has proved successful in discriminating when the mathematical pilot can or cannot separate rigid from elastic response in the tracking task.

Swaim, R. L.↗

NASA NTRS1976

A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer

A numerical study is made of the temporal eigenvalue spectrum of the Orr-Sommerfeld equation for the Blasius boundary layer. Unlike channel flows, there is no mathematical proof that this flow has an infinite spectrum of discrete eigenvalues. The Orr-Sommerfeld equation is integrated numerically, and the eigenvalues located by tracing out the contour lines in the complex wave velocity plane on which the real and imaginary parts of the secular determinant are zero. The spectrum of plane Poiseuille flow is used as a guide to study the spectrum of an artificial two-wall flow which consists of two Blasius boundary layers. As the upper boundary of this flow moves to infinity, it is found that the portion of the spectrum with an infinite number of eigenvalues moves towards phase velocity equal to unity and the spacing between eigenvalues goes to zero. The original few eigenvalues found are the only discrete eigenvalues that exist for Blasius flow.

Mack, L. M.↗

NASA NTRS1970

Effect of filtering on noise and timing in nuclear particle detection

The relations between signal shaping, noise, and timing resolution in nuclear particle detection systems are examined in this paper. Mathematical analysis of five commonly used types of filters leads to numerical results for system noise components arising from sources in the preamplifier, detector, and bias resistors. These results are presented in the form of design curves for the various filters, showing the dependence of each output noise component on both the magnitude of the noise sources and the filter time constants. Three of the filters considered are simple RC types; the remaining two are combinations of delay lines and RC elements. The quantitative calculations specifically assume a silicon detector and a field-effect-transistor preamplifier. Those filters that exhibit bipolar step response are analyzed in terms of crossover timing resolution, based on the earlier noise calculations. Again, the results are summarized in sets of design curves for each filter. Finally, the comparative performance of the various filter types is discussed, and specific examples are given.

Gary, S. A.↗

NASA NTRS1976

Biostereometric analysis of body form - The second manned Skylab mission

Results of biostereometric analyses of the body form of the Skylab 3 crew before and after flight. The Cartesian coordinates of numerous points on the body surface were derived by stereophotogrammetry, and mathematical analysis of the coordinate description allowed computation of the surface area and volume of the body, the volume of body segments, and the area and shape of cross sections. The weight loss in all three crew members was accompanied by a loss in volume distributed between the trunk and legs, with the legs showing the greatest proportional loss. The observed loss of volume apparently resulted from a combined loss of fluid in the abdomen and legs, of muscle in the legs and paraspinal region, and of fat in the abdomen and buttocks.

Whittle, M. W.↗

NASA NTRS1981

Calculation of two-dimensional inlet flow fields by an implicit method including viscous effects: User's manual

Inlet flow fields for airbreathing missiles are calculated by the adaptation of a two dimensional computational method developed for the flow around airfoils. A supersonic free stream is assumed to allow the forebody calculation to be uncoupled from the inlet calculation. The inlet calculation employs an implicit, time marching finite difference procedure to solve the thin layer Navier-Stokes equations formulated in body fitted coordinates. The mathematical formulation of the problem and the solution algorithm are given. Numerical stability and accuracy as well as the initial and boundary conditions used are discussed. Instructions for program use and operation along with the overall program logic are also given.

Biringen, S.↗

NASA NTRS1981

Computer simulation and experimental validation of isoelectric focusing in ampholine-free systems

An abbreviated version of a mathematical model of the steady state in isoelectric focusing is presented. Details of the mathematical transformations leading to a model suitable for computer implementation and numerical solution are given in the Appendix. The model describes the structure of concentration, pH, conductivity and potential gradients arising from the focusing of electrochemically defined ampholytes. Some of the results of computer simulations of two and three component systems are of particular interest to the experimentalist and are presented together with experimental validation of this model.

Bier, M.↗

NASA NTRS1988

Cracking of a layered medium on an elastic foundation under thermal shock

The cladded pressure vessel under thermal shock conditions which is simulated by using two simpler models was studied. The first model (Model 1) assumes that, if the crack size is very small compared to the vessel thickness, the problem can be treated as a semi-infinite elastic medium bonded to a very thin layer of different material. However, if the crack size is of the same order as the vessel thickness, the curvature effects may not be negligible. In this case it is assumed that the relatively thin walled hollow cylinder with cladding can be treated as a composite beam on an elastic foundation (Model 2). In both models, the effect of surface cooling rate is studied by assuming the temperature boundary condition to be a ramp function. The calculated results include the transient temperature, thermal stresses in the uncracked medium and stress intensity factors which are presented as a function of time, and the duration of cooling ramp. The stress intensity factors are also presented as a function of the size and the location of the crack. The problem is solved for two bonded materials of different thermal and mechanical properties. The mathematical formulation results in two singular integral equations which are solved numerically. The results are given for two material pairs, namely an austenitic steel layer welded on a ferritic steel substrate, and a ceramic coating on ferritic steel. In the case of the yielded clad, the stress intensity factors for a crack under the clad are determined by using a plastic strip model and are compared with elastic clad results.

Rizk, Abd El-Fattah A.↗

NASA NTRS1989

Recent developments in large-scale structural optimization

A brief discussion is given of mathematical optimization and the motivation for the development of more recent numerical search procedures. A review of recent developments and issues in multidisciplinary optimization is also presented. These developments are discussed in the context of the preliminary design of aircraft structures. A capability description of programs FASTOP, TSO, STARS, LAGRANGE, ELFINI and ASTROS is included.

Venkayya, Vipperla B.↗

NASA NTRS1991

Verification Of Tooling For Robotic Welding

Computer simulations, robotic inspections, and visual inspections performed to detect discrepancies. Method for verification of tooling for robotic welding involves combination of computer simulations and visual inspections. Verification process ensures accuracy of mathematical model representing tooling in off-line programming system that numerically simulates operation of robotic welding system. Process helps prevent damaging collisions between welding equipment and workpiece, ensures tooling positioned and oriented properly with respect to workpiece, and/or determines whether tooling to be modified or adjusted to achieve foregoing objectives.

Osterloh, Mark R.↗

NASA NTRS1992

Development Of Maneuvering Autopilot For Flight Tests

Report describes recent efforts to develop automatic control system operating under supervision of pilot and making airplane follow prescribed trajectories during flight tests. Report represents additional progress on this project. Gives background information on technology of control of test-flight trajectories; presents mathematical models of airframe, engine and command-augmentation system; focuses on mathematical modeling of maneuvers; addresses design of autopilots for maneuvers; discusses numerical simulation and evaluation of results of simulation of eight maneuvers under control of simulated autopilot; and presents summary and discussion of future work.

Menon, P. K. A.↗

NASA NTRS1993

Mathmatical modeling for diffractive optics

We consider a 'diffractive optic' to be a biperiodic surface separating two half-spaces, each having constant constitutive parameters; within a unit cell of the periodic surface and across the transition zone between the two half-spaces, the constitutive parameters can be a continuous, complex-valued function. Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the 'direct' problem and for the 'inverse' problem. In problems of the 'direct' class, the diffractive optic is specified, and the full set of Maxwell's equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. An example of a metallic grating at a Wood anomaly is presented as a case where other approaches are known to have convergence problems. In problems of the 'inverse' class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. Two approaches are described: phase reconstruction in the far-field approximation; and relaxed optimal design based on the Helmholtz equation. Practical examples are discussed for each approach to the inverse problem, including array generators in the far-field case and antireflective structures for the relaxed optimal design.

Dobson, David↗