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NASA NTRS1996

Mixing and Transition Control Studied

Considerable progress in understanding nonlinear phenomena in both unbounded and wallbounded shear flow transition has been made through the use of a combination of high- Reynolds-number asymptotic and numerical methods. The objective of this continuing work is to fully understand the nonlinear dynamics so that ultimately (1) an effective means of mixing and transition control can be developed and (2) the source terms in the aeroacoustic noise problem can be modeled more accurately. Two important aspects of the work are that (1) the disturbances evolve from strictly linear instability waves on weakly nonparallel mean flows so that the proper upstream conditions are applied in the nonlinear or wave-interaction streamwise region and (2) the asymptotic formulations lead to parabolic problems so that the question of proper out-flow boundary conditions--still a research issue for direct numerical simulations of convectively unstable shear flows--does not arise. Composite expansion techniques are used to obtain solutions that account for both mean-flow-evolution and nonlinear effects. A previously derived theory for the amplitude evolution of a two-dimensional instability wave in an incompressible mixing layer (which is in quantitative agreement with available experimental data for the first nonlinear saturation stage for a plane-jet shear layer, a circular-jet shear layer, and a mixing layer behind a splitter plate) have been extended to include a wave-interaction stage with a three-dimensional subharmonic. The ultimate wave interaction effects can either give rise to explosive growth or an equilibrium solution, both of which are intimately associated with the nonlinear self-interaction of the three dimensional component. The extended theory is being evaluated numerically. In contrast to the mixing-layer situation, earlier comparisons of theoretical predictions based on asymptotic methods and experiments in wall-bounded shear-flow transition have been somewhat lacking in one aspect or another. The current work strongly suggests that the main weakness is the underlying asymptotic representation of the linear "part" of the problem and not the explicit modeling of the nonlinear/wave-interaction effects. Consequently, the long-wave-length/high-Reynolds-number asymptotic limit for the Blasius boundary-layer stability problem was reexamined, and a new dispersion relationship for the instability waves that is uniformly valid for both the upper- and lower branch regions to the required order of approximation was obtained. A comparison with numerical results, obtained by solving the Orr-Sommerfeld stability problem, shows that the asymptotic formula provides surprisingly good results, even for values of the frequency parameter usually encountered in experimental investigations. This is particularly evident in the dynamically important upper-branch region, where much of the nonlinear interactions in transition experiments are believed to take place. The result is important in that it can be used to greatly improve the accuracy of weakly nonlinear critical-layer-based theories, and a consistent nonlinear theory is currently under evaluation.

Source record↗

NASA NTRS2002

Trajectories for High Specific Impulse High Specific Power Deep Space Exploration

Flight times and deliverable masses for electric and fusion propulsion systems are difficult to approximate. Numerical integration is required for these continuous thrust systems. Many scientists are not equipped with the tools and expertise to conduct interplanetary and interstellar trajectory analysis for their concepts. Several charts plotting the results of well-known trajectory simulation codes were developed and are contained in this paper. These charts illustrate the dependence of time of flight and payload ratio on jet power, initial mass, specific impulse and specific power. These charts are intended to be a tool by which people in the propulsion community can explore the possibilities of their propulsion system concepts. Trajectories were simulated using the tools VARITOP and IPOST. VARITOP is a well known trajectory optimization code that involves numerical integration based on calculus of variations. IPOST has several methods of trajectory simulation; the one used in this paper is Cowell's method for full integration of the equations of motion. An analytical method derived in the companion paper was also evaluated. The accuracy of this method is discussed in the paper.

Polsgrove, Tara↗

NASA NTRSDate not supplied

Evidence of High-Angle Ejecta from Impacts Iinto Various Granular Materials

The dominant mechanism for resurfacing airless bodies is the excavation and ejection of material during the formation of impact craters. Ejecta that is deposited proximal to the rim of craters formed in the gravity-regime (where gravitational forces are greater than material strength) form a relatively smooth and continuous deposit. Aside from far-field secondary craters, craters observed on continuous ejecta deposits are mostly assumed to be representative of the primary impactor flux after the time of deposition. Sustained primary bombardment should produce a homogeneous crater population across this surface, thus providing an opportunity to determine crater size-frequency distributions and surface chronologies. Deviations from this ideal have been observed as different crater-size distributions appearing between the continuous deposits and their superimposed melt ponds. Numerous explanations for this discrepancy have been proposed, one of which is the occurrence of self-secondary craters, which would be created by ejecta launched at sufficiently high-angles to re-impact the fresh continuous ejecta deposits. Here, we present results from cratering experiments to explore the influence of density, porosity, and friction on ejecta kinematics and report on the observation of such high-angle ejecta in cohesionless granular targets.

Impact crater↗

NASA NTRS1995

Annual Research Briefs: 1995

This report contains the 1995 annual progress reports of the Research Fellows and students of the Center for Turbulence Research (CTR). In 1995 CTR continued its concentration on the development and application of large-eddy simulation to complex flows, development of novel modeling concepts for engineering computations in the Reynolds averaged framework, and turbulent combustion. In large-eddy simulation, a number of numerical and experimental issues have surfaced which are being addressed. The first group of reports in this volume are on large-eddy simulation. A key finding in this area was the revelation of possibly significant numerical errors that may overwhelm the effects of the subgrid-scale model. We also commissioned a new experiment to support the LES validation studies. The remaining articles in this report are concerned with Reynolds averaged modeling, studies of turbulence physics and flow generated sound, combustion, and simulation techniques. Fundamental studies of turbulent combustion using direct numerical simulations which started at CTR will continue to be emphasized. These studies and their counterparts carried out during the summer programs have had a noticeable impact on combustion research world wide.

Source record↗

NASA NTRS1972

6300 A quantum efficiency of the recombination mechanism in the night-time F layer.

Simultaneous airglow and electron content measurements made at Hawaii are used to infer the number of 6300 and 6364 A quanta produced per electron lost in the nighttime F layer of the ionosphere. The equation of continuity of electrons is then solved numerically to obtain the electron density profile, and the amount of quenching is estimated. This leads to the number of excitations of O(super-1 D) per O2(+) recombination (epsilon). We find, for an exospheric temperature of 1100 K, epsilon is equal to 1.1 plus or minus 0.6, in good agreement with Zipf's laboratory measurement at 300 K.

Brown, W. E.↗

NASA NTRS1975

Liquid jet pumped by rising gas bubbles

A two-phase mathematical model is proposed for calculating the induced turbulent vertical liquid flow. Bubbles provide a large buoyancy force and the associated drag on the liquid moves the liquid upward. The liquid pumped upward consists of the bubble wakes and the liquid brought into the jet region by turbulent entrainment. The expansion of the gas bubbles as they rise through the liquid is taken into account. The continuity and momentum equations are solved numerically for an axisymmetric air jet submerged in water. Water pumping rates are obtained as a function of air flow rate and depth of submergence. Comparisons are made with limited experimental information in the literature.

Hussain, N. A.↗

NASA NTRS1975

Liquid jet pumped by rising gas bubbles

From observations of a stream of gas bubbles rising through a liquid, a two-phase mathematical model is proposed for calculating the induced turbulent vertical liquid flow. The bubbles provide a large buoyancy force and the associated drag on the liquid moves the liquid upward. The liquid pumped upward consists of the bubble wakes and the liquid brought into the jet region by turbulent entrainment. The expansion of the gas bubbles as they arise through the liquid is taken into account. The continuity and momentum equations are solved numerically for an axisymmetric air jet submerged in water. Water pumping rates are obtained as a function of air flow rate and depth of submergence. Comparisons are made with limited experimental information in the literature.

Hussain, N. A.↗

NASA NTRS1975

A computer program for fitting smooth surfaces to three-dimensional aircraft configurations

A computer program developed to fit smooth surfaces to the component parts of three-dimensional aircraft configurations was described. The resulting equation definition of an aircraft numerical model is useful in obtaining continuous two-dimensional cross section plots in arbitrarily defined planes, local tangents, enriched surface plots and other pertinent geometric information; the geometry organization used as input to the program has become known as the Harris Wave Drag Geometry.

Craidon, C. B.↗

NASA NTRS1976

A limiting analysis for edge effects in angle-ply laminates

A zeroth order solution for edge effects in angle ply composite laminates using perturbation techniques and a limiting free body approach was developed. The general method of solution for laminates is developed and then applied to the special case of a graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness to width ratio h/b and compared to existing numerical results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress for two laminates, and provides mathematical evidence for singular interlaminar shear stresses.

Hsu, P. W.↗

NASA NTRS1980

The compatible balancing approach to initialization, and four-dimensional data assimilation

A unified theoretical approach to both the four-dimensional assimilation of asynoptic data and the initialization problem is attempted. This approach relies on the derivation of certain relationships between geopotential tendencies and tendencies of the horizontal velocity field in primitive-equation models of atmospheric flow. The approach is worked out and analyzed in detail for some simple barotropic models. Certain independent results of numerical experiments for the time-continuous assimilation of real asynoptic meteorological data into a complex, baroclinic weather prediction model are discussed in the context of the present approach. Tentative inferences are drawn for practical assimilation procedures.

Ghil, M.↗

NASA NTRS1982

Seasonal variations of the high-latitude F region for strong convection

A plasma convection model is combined with an ionospheric-atmospheric composition model in order to study the seasonal variations of the high-latitude F region for geomagnetic conditions leading to strong convection. In a model calculation, a field tube of plasma is followed as it moves along a convection trajectory through a moving neutral atmosphere. Altitude profiles of the ion densities are obtained by solving the appropriate continuity, momentum, and energy equations including numerous high-latitude processes. It is found that the high-latitude ionosphere exhibits a significant UT variation both during the winter and summer. In general, the electron density at high-latitudes is lower in winter than in summer. In both summer and winter, the major region of low electron density is associated with the 'main' or mid-latitude' trough.

Sojka, J. J.↗

NASA NTRS1984

Transformation of two and three-dimensional regions by elliptic systems

The research during this period continued to expand the class of numerical algorithms that can be accurately and efficiently implemented on overlapping grids. Whereas previous calculations have been used to solve elliptic equations and to find the steady-state solution of parabolic equations, the present work is aimed towards developing time-accurate solution techniques for parabolic and hyperbolic equations. The primary difficulty here is in the correct treatment of the interior boundary nodes that must be updated at each iteration. The implementation of explicit methods is straightforward. However, the common practice of lagging these values when using an implicit methods leads to inconsistencies in the difference equation. One way to avoid this problem is to alternately calculate with an implicit and an explicit method on each subgrid. With this procedure, the explicit method generates boundary values at the next time level which are then used by the implicit step. It can be shown that when a backward implicit method is combined with a forward explicit method, the composite method is second order accurate and unconditionally stable for linear problems. A second area in which progress can be reported is in the distribution of grid points on curves and surfaces.

Mastin, E. W.↗

NASA NTRS1991

Charge collected by diffusion from an ion track under mixed boundary conditions

Charge-carrier diffusion from an ion track in a silicon substrate at least a few hundred microns thick is analyzed. The substrate upper surface is treated as reflective except for a small section, intended to represent a reverse-biased junction, which is treated as a sink. Total charge collected by the sink is calculated by assuming transport to be governed by an ambipolar diffusion equation with temporally constant and spatially uniform carrier lifetime and diffusion coefficient. Present results apply to a normally incident track but could easily be generalized to arbitrary track direction. The collected charge is found to depend on track length and on the electrostatic capacitance, rather than the area, of the sink. Theoretical predictions are compared to the results of a numerical simulation called the Poisson and Continuity Equation Solver (PISCES) for three cases and are found to agree within a factor of two in the worst case.

Edmonds, Larry D.↗

NASA NTRS1993

Effects of a parallel electric field and the geomagnetic field in the topside ionosphere on auroral and photoelectron energy distributions

The consequences of electric field acceleration and an inhomogeneous magnetic field on auroral electron energy distributions in the topside ionosphere are investigated. The one-dimensional, steady state electron transport equation includes elastic and inelastic collisions, an inhomogeneous magnetic field, and a field-aligned electric field. The case of a self-consistent polarization electric field is considered first. The self-consistent field is derived by solving the continuity equation for all ions of importance, including diffusion of O(+) and H(+), and the electron and ion energy equations to derive the electron and ion temperatures. The system of coupled electron transport, continuity, and energy equations is solved numerically. Recognizing observations of parallel electric fields of larger magnitude than the baseline case of the polarization field, the effect of two model fields on the electron distribution function is investigated. In one case the field is increased from the polarization field magnitude at 300 km to a maximum at the upper boundary of 800 km, and in another case a uniform field is added to the polarization field. Substantial perturbations of the low energy portion of the electron flux are produced: an upward directed electric field accelerates the downward directed flux of low-energy secondary electrons and decelerates the upward directed component. Above about 400 km the inhomogeneous magnetic field produces anisotropies in the angular distribution of the electron flux. The effects of the perturbed energy distributions on auroral spectral emission features are noted.

Min, Q.-L.↗

NASA NTRS1995

Design, construction and testing of annular diffusers for high speed civil transportation combustor applications

A theoretical and an experimental design study of subsonic flow through curved-wall annular diffusers is being carried out in order to establish the most pertinent design parameters for such devices and the implications of their application in the design of engine components in the aerospace industries. This investigation consists of solving numerically the full Navier Stokes and Continuity equations for the time-mean flow. Various models of turbulence are being evaluated for adoption throughout the study and comparisons would be made with experimental data where they exist. Assessment of diffuser performance based on the dissipated mechanical energy would also be made. The experimental work involves the application of Computer Aided Design software tool to the development of a suitable annular diffuser geometry and the subsequent downloading of such data to a CNC machine at Central State University. The results of the investigations are expected to indicate that more cost effective component design of such devices as effective component design of such devices as diffusers which normally contain complex flows can still be achieved. In this regard a review paper was accepted and presented at the First International Conference on High Speed Civil Transportation Research held at North Carolina A&T in December of 1994.

Okhio, Cyril B.↗

NASA NTRS1993

Effects of a Parallel Electric Field and the Geomagnetic Field in the Topside Ionosphere on Auroral and Photoelectron Energy Distributions

The consequences of electric field acceleration and an inhomogencous magnetic field on auroral electron energy distributions in the topside ionosphere are investigated. The one- dimensional, steady state electron transport equation includes elastic and inelastic collisions, an inhomogencous magnetic field, and a field-aligned electric field. The case of a self-consistent polarization electric field is considered first. The self-consistent field is derived by solving the continuity equation for all ions of importance, including diffusion of 0(+) and H(+), and the electron and ion energy equations to derive the electron and ion temperatures. The system of coupled electron transport, continuity, and energy equations is solved numerically. Recognizing observations of parallel electric fields of larger magnitude than the baseline case of the polarization field, the effect of two model fields on the electron distribution function in investigated. In one case the field is increased from the polarization field magnitude at 300 km to a maximum at the upper boundary of 800 km, and in another case a uniform field is added to the polarization field. Substantial perturbations of the low energy portion of the electron flux are produced: an upward directed electric field accelerates the downward directed flux of low-energy secondary electrons and decelerates the upward directed component. Above about 400 km the inhomogencous magnetic field produces anisotropies in the angular distribution of the electron flux. The effects of the perturbed energy distributions on auroral spectral emission features are noted.

Min, Q.-L.↗

NASA NTRS2012

A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation

Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.

integration↗

NASA NTRS2002

Validated Numerical Models for the Convective Extinction of Fuel Droplets (CEFD)

The NASA Nebraska Space Grant (NSGC) & EPSCoR programs have continued their effort to support outstanding research endeavors by funding the Numerical Simulation of the Combustion of Fuel Droplets study at the University of Nebraska at Lincoln (UNL). This team of researchers has developed a transient numerical model to study the combustion of suspended and moving droplets. The engines that propel missiles, jets, and many other devices are dependent upon combustion. Therefore, data concerning the combustion of fuel droplets is of immediate relevance to aviation and aeronautical personnel, especially those involved in flight operations. The experiments being conducted by Dr. Gogos and Dr. Nayagam s research teams, allow investigators to gather data for comparison with theoretical predictions of burning rates, flame structures, and extinction conditions. The consequent improved fundamental understanding of droplet combustion may contribute to the clean and safe utilization of fossil fuels (Williams, Dryer, Haggard & Nayagam, 1997, f 2). The present state of knowledge on convective extinction of fuel droplets derives from experiments conducted under normal gravity conditions. However, any data obtained with suspended droplets under normal gravity are grossly affected by gravity. The need to obtain experimental data under microgravity conditions is therefore well justified and addresses one of the goals of NASA's Human Exploration and Development of Space (HEDS) microgravity combustion experiment.

Gogos, George↗