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A mathematical model for a two-phase flow laminar airfoil in simulated heavy rain has been established. The set of non-linear partial differential equations has been converted into a set of finite difference equations; appropriate initial and boundary conditions are provided. The numerical results are compared with the experimental measurements. They show good agreement in quality.
We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.
Work has included significant research in several areas aimed at further clarification of the aging and chemical failure mechanism of thermoplastics (PVDF or Tefzel) for pipes. Among the areas investigated were the crystallinity changes associated with both the Coflon and Tefzel after various simulated environmental exposures using X-Ray diffraction analysis. We have found that significant changes in polymer crystallinity levels occur as a function of the exposures. These crystallinity changes may have important consequences on the fracture, fatigue, tensile, and chemical resistance of the materials. We have also noted changes in the molecular weight distribution of the Coflon material using a dual detector Gel Permeation Analysis. Again these changes may result in variation in the mechanical and chemical properties in the material. We conducted numerous analytical studies with methods including X-Ray Diffraction, Gel Permeation Chromatography, Fourier Transform Infrared Spectroscopy, Thermogravimetric Analysis, and Differential Scanning Calorimetry. We investigated a number of aged samples of both Tefzel and Coflon that were forwarded from MERL. Pressurized tests were performed in a modified Fluid G, which we will call G2. In this case the ethylene diamine concentration was increased to 3 percent in methanol. Coflon pipe sections and powdered Coflon were exposed in pressure cells at 1700 psi at three separate test temperatures, 70 C, 110 C, and 130 C. The primary purpose of the pressure tests in Fluid G2 was to further elucidate the aging mechanism of PVDF degradation.
The objective of this research is to develop and implement new methodology for large eddy simulation of (LES) of high-speed reacting turbulent flows. We have just completed two (2) years of Phase I of this research. This annual report provides a brief and up-to-date summary of our activities during the period: September 1, 2000 through August 31, 2001. In the work within the past year, a methodology termed "velocity-scalar filtered density function" (VSFDF) is developed and implemented for large eddy simulation (LES) of turbulent flows. In this methodology the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function (PDF) of all of the components of the velocity and scalar vectors. An exact transport equation is derived for the VSFDF in which the effects of the unresolved SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source terms appear in closed form. The remaining unclosed terms in this equation are modeled. A system of stochastic differential equations (SDEs) which yields statistically equivalent results to the modeled VSFDF transport equation is constructed. These SDEs are solved numerically by a Lagrangian Monte Carlo procedure. The consistency of the proposed SDEs and the convergence of the Monte Carlo solution are assessed by comparison with results obtained by an Eulerian LES procedure in which the corresponding transport equations for the first two SGS moments are solved. The unclosed SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source in the Eulerian LES are replaced by corresponding terms from VSFDF equation. The consistency of the results is then analyzed for a case of two dimensional mixing layer.
Studies were performed to carry out semi-empirical validation of a new measurement approach we propose for molecular mixing ratios determination. The approach is based on relative measurements in bands of O2 and other molecules and as such may be best described as cross band relative absorption (CoBRA). . The current validation studies rely upon well verified and established theoretical and experimental databases, satellite data assimilations and modeling codes such as HITRAN, line-by-line radiative transfer model (LBLRTM), and the modern-era retrospective analysis for research and applications (MERRA). The approach holds promise for atmospheric mixing ratio measurements of CO2 and a variety of other molecules currently under investigation for several future satellite lidar missions. One of the advantages of the method is a significant reduction of the temperature sensitivity uncertainties which is illustrated with application to the ASCENDS mission for the measurement of CO2 mixing ratios (XCO2). Additional advantages of the method include the possibility to closely match cross-band weighting function combinations which is harder to achieve using conventional differential absorption techniques and the potential for additional corrections for water vapor and other interferences without using the data from numerical weather prediction (NWP) models.
GMO dwarf plum (Prunus domestica) is being evaluated as a candidate food crop for long duration space flight missions. A project was undertaken to develop a protocol for transferring selected genetic lines of GMO plum (previously maintained in pots and propagated by cuttings at NASA's Kennedy Space Center in Florida) into in vitro tissue culture. In vitro culture may reduce the space, materials, and labor required to maintain the current lines of GMO plum and better preserve them for future study. Fresh plant material from three selected GMO plum lines (NASA-5, NASA-10, and NASA-11) and a non-modified control line (Control-5) were processed aseptically into in vitro culture on four separate occasions. The impact of multiple treatments on the successful growth of GMO plum tissue in vitro were tested: Parent explant tissue type (leaf petioles, stem nodes containing buds and internodes without buds), tissue sterilization method [soaking in 10 bleach only (5 min for petioles or 10 min for nodesinternodes), or soaking in 70 EtOH (30 sec) followed by 10 bleach (5 min for petioles and 10 min for nodesinternodes)], and media type [three Murashige and Skoog-based medias (SGM, SRM, and SRM+2,4-D) and one recipe containing woody plant media (WPM)]. 22.2 of the plates containing tissue sterilized with bleach alone developed microbial contamination after two weeks, while only 11.8 of plates containing tissue sterilized sequentially with EtOH and bleach developed contamination. Node bud tissue from all four genetic lines of plum produced leafy plantlets on SGM and SRM media after 4-6 weeks. The most numerous and well-developed plantlets were present on SGM. Upon reaching suitable size, plantlets were transferred to larger media containers for further growth. Some node bud growth occurred on SRM+2,4-D and WPM 2.5 weeks after plating, however as of yet no pieces on SRM+2,4-D have adequate development for transferring. Tissue pieces from NASA-5 plated on WPM are developing leaves and will be ready for transferring soon. Petioles and internode tissue lacking bud meristem failed to produce any plantlets on any plates, however petioles developed large masses of undifferentiated callus tissue on SRM+2,4-D media. These callused pieces were then transferred to SRM+TDZ media, which resulted in even larger callus growth but no differentiation. All four selected plum lines were successfully transitioned into in vitro culture. Nodes from NASA-5 and NASA-10 lines produced the most numerous and well-developed leafy plantlets in vitro, while those from NASA-11 and Control-5 were generally smaller, slower growing and less numerous. The best method overall was to use young stem node tissue with buds, surface sterilize the pieces sequentially with 70 EtOH and 10 bleach, and then plate them onto SGM media. Future areas of study will include introducing additional genetic lines of GMO plum into in vitro culture, attempting to induce shoot growth in petiole callus tissue, testing methods (such as cold storage) that extend the time interval between transferring explants into new media, and testing viability of plantlets transferred from in vitro culture back to traditional pot culture.
Study illustrating how the presence of a high-intensity pulse of radiation can distort its own passage through a plane differentially shearing medium. It is demonstrated that the distortion is a sensitive function of the precise, and detailed, variation of the medium's refractive index by considering a couple of simple examples which are worked out numerically. In view of the high-intensity pulses observed from pulsars (approximately 10 to the 30th ergs per pulse), it is believed that the present calculations are of more than academic interest in helping unravel the fundamental properties of pulse production in, and propagating through, differentially sheared media - such as pulsars' magnetospheres within the so-called speed-of-light circle.
Runge-Kutta type formulas applied to restricted three-body problem achieving high order accuracy by m-fold differentiation and simple transformation
The general nonlinear discretized equations of motion of spinning elastic solids and structures are derived as a set of nonlinear ordinary differential equations for the case when the strain-displacement and velocity-displacement relations are nonlinear up to the second order. It is shown that the cost of generation of such equations is proportional to the fourth power of the number of degrees of freedom. A computer program is written to automatically generate the equations for the case of spinning cantilevers with initial imperfections. The types and the number of the coordinate functions used in the trial solution are parameters of the program.
The transient performance of ablation type heat protection shields is treated herein for the surface of a vehicle returning from outer space to the earth. The vehicle weighs 8640 kg, has a ballistic factor of 500 lb/ft2, re-enters with a speed of 11 km/sec at 120 km altitude, has a lift over drag ratio of -0.5, and is subjected to a maximum deceleration of 7.7 times the gravity constant. By use of well-known equations for the heat transfer and the mass transfer at a heated surface, a numerical calculation method is derived which, for the investigated ablation processes, yields exact transient solutions of the fundamental system of partial differential equations. The method is applied to various quartz shields and to one Teflon shield, which all evaporate so readily under the conditions of the problem at hand that practically no flow of molten shield material exists. The solutions also show comparatively small temperature changes parallel to the surface. The results show that the nose of the vehicle is cooled predominantly by the evaporation of the quartz or the Teflon; the rest of the vehicle's surface is cooled by radiation of the quartz or evaporation of the Teflon. The large mass transfer effects on the nose of the vehicle are detrimental since the resulting low surface temperatures prevent the radiative heat transfer out of the shield, which does not involve any mass loss, from being the desirable governing cooling factor.
Analysis of electromagnetic fields in inhomogeneous media is of practical interest in general scattering and propagation problems and in the study of lenses. For certain types of inhomogeneities, the fields may be represented in terms of two scalars. In a general orthogonal coordinate system, these potentials satisfy second order differential equations. Exact solutions of these equations are known only for a few particular cases and in general, an approximate or numerical technique must be employed. The present work reviews and generalizes some of the main methods of attack of the problem. The results are presented in a form appropriate for numerical computation.
A finite element algorithm is derived for the numerical solution of a three-dimensional flow field described by a system of initial-valued, elliptic boundary value partial differential equations. The familiar three-dimensional boundary layer equations belong to this description when diffusional processes in only one coordinate direction are important. The finite element algorithm transforms the original description into large order systems of ordinary differential equations written for the dependent variables discretized at node points of an arbitrarily irregular computational lattice. The generalized elliptic boundary conditions is piecewise valid for each dependent variable on boundaries that need not explicitly coincide with coordinate surfaces. Solutions for sample problems in laminar and turbulent boundary flows illustrate favorable solution accuracy, convergence, and versatility.
We give a detailed discussion of the group-velocity ray paths in a plane differentially sheared medium with constant index of refraction as measured by a local inertial observer. For a given velocity profile the numerical ray paths are presented graphically for several representative cases. Assuming that the medium has a volume emissivity and that a given flux of radiation is incident at the base of the medium, the flux of radiation leaving the slab as a function of exit angle is calculated and presented in the same representative cases. Peaks and discontinuities in the flux generally appear at given exit angles, but their locations and the half-widths of the peaks depend sensitively on the index of refraction.
The objective was to try to develop a useful numerical algorithm for the Drazin inverse and to analyze the numerical aspects of the applications of the Drazin inverse relating to the study of homogeneous Markov chains and systems of linear differential equations with singular coefficient matrices. It is felt that all objectives were accomplished with a measurable degree of success.
Numerical algorithms for analysis and design of large space structures are investigated. The sign algorithm and its application to decoupling of differential equations are presented. The generalized sign algorithm is given and its application to several problems discussed. The Laplace transforms of matrix functions and the diagonalization procedure for a finite element equation are discussed. The diagonalization of matrix polynomials is considered. The quadrature method and Laplace transforms is discussed and the identification of linear systems by the quadrature method investigated.
Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.
There is considerable interest in developing a numerical scheme for solving the time dependent viscous compressible three dimensional flow to aid in the design of helicopter rotors. Numerical algorithms are examined to determine their overall suitability for the efficient and routine solution of an appropriate system of partial differential equations. It is concluded that a consistently split time linearized block implicit scheme using either quintic B spline collocation or the generalized operator compact implicit approach to generate a fourth order accurate algorithm is particularly well suited for use on the present problem. High cell Reynolds number behavior leads to favoring the generalized operator compact implicit approach over the quintic B spline collocation method.
The effect of downburst-type wind shears on the longitudinal dynamic behavior of an unguided aircraft is simulated numerically on the basis of published meteorological data and the flight characteristics of an A300-B passenger jet. The nonlinear differential equations of the aircraft motion are linearized by conventional methods, and the wind effects are introduced via the linear derivatives of the wind components referred to the wind gradients to obtain simplified technical models of the longitudinal response to all possible types of constant-gradient wind shears during the first 20-60 sec. Graphs, maps, and diagrams are provided, and a number of accidents presumed to have involved wind shears are analyzed in detail.