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Results for “exponential growth”

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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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Shock tube study of the reaction H plus O2 plus Ar yields HO2 plus Ar

Rate coefficient data for the recombination reaction H + 02 + Ar yields H02 + Ar have been determined from studies of lean hydrogen-oxygen mixtures behind incident shock waves over the temperature range of 948 to 1125 K. Hydroxyl radical concentration profiles were measured by ultraviolet absorption spectroscopy, and rate data were obtained through analysis of induction time and exponential growth parameter data. Analysis of the data yielded a rate coefficient which was generally lower than most of the more recent values obtained from shock tube studies. The effect of boundary layer formation on the conditions behind the shock was also examined and found to be negligible.

Jachimowski, C. J.↗
NASA NTRS1974

Shock tube measurements of specific reaction rates in the branched chain CH4-CO-O2 system

Rate constants of two elementary bimolecular reactions involved in the oxidation of methane have been determined by monitoring the exponential growth of CO flame band emission behind incident shocks in three suitably chosen gas mixtures. The data do not support a mechanism which invokes the four center process CH3 + O2 yields CH2O + OH for the reaction of methyl with oxygen.

Brabbs, T. A.↗
NASA NTRS1976

The dilemma of future electric power demand

Dim prospects are held out for continued exponential growth rates in the generation and use of electric power worldwide and in many local areas, extrapolating from current trends and common projections. While acknowledging the unique advantages of electric power use, the article points out the 30% level of efficiency in conversion of other forms of energy to electrical energy, with huge volumes of wasted energy plus thermal pollution. Even growth at a fixed rate is found problematical, with future needs exhausting water and land resources and fossil fuels in time. Alleviation of the situation by shifting much of the load to still unproven technologies is considered cautiously

Wu, Y.-C.↗
NASA NTRS1978

Physical properties of the planets and satellites from radar observations

The radar cross section of a planetary target is defined as the area of an isotropic scatterer, normal to the illumination, that would yield the observed echo intensity, if it were placed at the target's location. Attention is given to the angular scattering law, surface imagery, and topography. The observational results are discussed, taking into account the moon and the inner planets, the asteroids, the Galilean satellites, and the rings of Saturn. It is pointed out that the reach of radar astronomy has maintained nearly an exponential growth over the past three decades, as the sensitivity of available radar systems has on average more than doubled each year. There are, however, limits to this growth set by the large costs required for a new generation of observing facilities. Only modest increases in radar system sensitivity are, therefore, expected for the next decade.

Pettengill, G. H.↗
NASA NTRS1983

Space Phase III - The commercial era dawns

After the 'Phase I' of space activities, the period bounded by Sputnik and Apollo, 'Phase II', has been entered, a phase in which concerns over the use and the protection of space assets which support national security predominate. However, it is only when the commercial motive becomes prominent that human activity in new regions truly prospers and enters periods of exponential growth. It is believed that there are increasing signs that such a period, called 'Space Phase III', may be coming soon. A description is presented of developments and results upon which this conclusion is based. Since 1980, there have been three developments of great importance for the future of space activities. Six highly successful flights have demonstrated that the Space Shuttle concept works. A series of Soviet missions are related to the emergence of a capability to construct and service modular space stations. Successful tests of the European Ariane 1 indicate an end to U.S. monopoly with respect to the provision of launch services to the Western World.

Allnutt, R. F.↗
NASA NTRS1985

Preparative electrophoresis of cultured human cells: Effect of cell cycle phase

Human epithelioid T-1E cells were cultured in suspension and subjected to density gradient electrophoresis upward in a vertical column. It is indicated that the most rapidly migrating cells were at the beginning of the cell cycle and the most slowly migrating cells were at the end of the cell cycle. The fastest migrating cells divided 24 hr later than the slowest migrating cells. Colonies developing from slowly migrating cells had twice as many cells during exponential growth as did the most rapidly migrating cells, and the numbers of cells per colony at any time was inversely related to the electrophoretic migration rate. The DNA measurements by fluorescence flow cytometry indicates that the slowest migrating cell populations are enriched in cells that have twice as much DNA as the fastest migrating cells. It is concluded that electrophoretic mobility of these cultured human cells declines steadily through the cell cycle and that the mobility is lowest at the end of G sub 2 phase and highest at the beginning of G sub 1 phase.

Kunze, M. E.↗
NASA NTRS1985

Size and DNA distributions of electrophoretically separated cultured human kidney cells

Electrophoretic purification of purifying cultured cells according to function presumes that the size of cycle phase of a cell is not an overriding determinant of its electrophoretic velocity in an electrophoretic separator. The size distributions and DNA distributions of fractions of cells purified by density gradient electrophoresis were determined. No systematic dependence of electrophoretic migration upward in a density gradient column upon either size or DNA content were found. It was found that human leukemia cell populations, which are more uniform function and found in all phases of the cell cycle during exponential growth, separated on a vertical sensity gradient electrophoresis column according to their size, which is shown to be strictly cell cycle dependent.

Kunze, M. E.↗
NASA NTRS1987

Generation of Tollmien-Schlichting waves on interactive marginally separated flows

This paper is concerned with the interaction of very-long-wavelength free-stream disturbances with the small but abrupt changes in the mean flow that occur near the minimum-skin-friction point in an interactive marginally separated boundary layer. The source frequency is chosen so that the eigensolutions with that frequency have an 'interactive' structure in the region of marginal separation. The eigensolution wavelength scale must then differ from the lengthscale of the marginal separation, and a composite expansion technique has to be used to obtain the solution. The initial instability wave amplitude turns out to be exponentially small, but eventually dominates the original disturbance owing to its exponential growth. It then begins to decay but ultimately turns into a standard spatially growing Tollmien-Schlichting wave much further downstream.

Goldstein, M. E.↗
NASA NTRS1987

Fast-dynamo action in unsteady flows and maps in three dimensions

Unsteady fast-dynamo action is obtained in a family of stretch-fold-shear maps applied to a spatially periodic magnetic field in three dimensions. Exponential growth of a mean field in the limit of vanishing diffusivity is demonstrated by a numerical method which alternates instantaneous deformations with molecular diffusion over a finite time interval. Analysis indicates that the dynamo is a coherent feature of the large scales, essentially independent of the cascade of structure to small scales.

Bayly, B. J.↗
NASA NTRS1986

On testing of functionally equivalent components of fault-tolerant software

Six functionally equivalent programs were tested with specification based random and extremal/special value (ESV) test cases. Statement and branch coverage were used to measure and compare the attained testing effectiveness. It was observed that both measures reached a nearly steady state value after 25 to 75 random test cases. Coverage saturation curves appear to follow an exponential growth model. However, the steady state values for branch coverage of different components, but the same input cases, differed by as much as 22 percent. The effect is the result of the differences in the detailed structure of the components. Improvement in coverage provided by the random test data, after the ESV cases were executed, was only about 1 percent. Results indicate that extensive random testing can be a process of diminishing returns, and that in the FTS context functional ('black box') testing can provide a very uneven execution coverage of the functionally equivalent software, and therefore should be supplemented by structure based testing.

Vouk, Mladen A.↗
NASA NTRS1990

Spectral simulation of unsteady compressible flow past a circular cylinder

An unsteady compressible viscous wake flow past a circular cylinder was successfully simulated using spectral methods. A new approach in using the Chebyshev collocation method for periodic problems is introduced. It was further proved that the eigenvalues associated with the differentiation matrix are purely imaginary, reflecting the periodicity of the problem. It was been shown that the solution of a model problem has exponential growth in time if improper boundary conditions are used. A characteristic boundary condition, which is based on the characteristics of the Euler equations of gas dynamics, was derived for the spectral code. The primary vortex shedding frequency computed agrees well with the results in the literature for Mach = 0.4, Re = 80. No secondary frequency is observed in the power spectrum analysis of the pressure data.

Don, Wai-Sun↗
NASA NTRS1989

Nonlinear interactions in mixing layers and compressible heated round jets

The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

Jarrah, Yousef Mohd↗
NASA NTRS1991

Resonant triad in boundary-layer stability. Part 1: Fully nonlinear interaction

A first principles theory is developed to study the nonlinear spatial evolution of a near-resonance triad of instability waves in boundary layer transition. This triad consists of a plane wave at fundamental frequency and a pair of symmetrical, oblique waves at the subharmonic frequency. A low frequency, high Reynolds number asymptotic scaling leads to a distinct critical layer where nonlinearity first becomes important; the development of the triad's waves is determined by the critical layer's nonlinear, viscous dynamics. The resulting theory is fully nonlinear in that all nonlinearly generated oscillatory and nonoscillatory components are accounted for. The presence of the plane wave initially causes exponential of exponential growth of the oblique waves. However, the plane wave continues to follow the linear theory, even when the oblique waves' amplitude attains the same order of magnitude as that of the plane wave. A fully interactive stage then comes into effect when the oblique waves exceed a certain level compared to that of the plane wave. The oblique waves react back on the fundamental, slowing its growth rate. The oblique waves' saturation results from their self-interaction - a mechanism that does not require the presence of the plane wave. The oblique waves' saturation level is independent of their initial level, but decreases as the obliqueness angle increases.

Mankbadi, Reda R.↗
NASA NTRS1990

Small error dynamics and the predictability of atmospheric flows

In this paper, linear small-error theory is applied to the study of weather predictability. A simple baroclinic shear model and a barotropic channel model with a localized jet are used as examples. It is shown that increase in error on synoptic forecast time scales is controlled by rapidly growing perturbations that are not of normal mode form. Unpredictable regimes are not necessarily associated with larger exponential growth rates than are relatively more predictable regimes. Model problems illustrating baroclinic and barotropic dynamics suggest that asymptotic measures of divergence in phase space, while applicable in the limit of infinite time, may not be appropriate over time intervals addressed by present synoptic forecast.

Farrell, Brian F.↗
NASA NTRS1990

Nonlinear spatial evolution of externally excited instability waves in free shear layers

The effects of critical-layer nonlinearity on spatially growing instability waves on shear layers between parallel streams are considered. In the two-dimensional incompressible case, the flow in the critical layer is governed by a nonequilibrium, nonlinear vorticity equation. The initial exponential growth of the instability wave is converted into algebraic growth during the streamwise 'aging' of the critical layer into a quasi-equilibrium state. This leads to a next stage of evolution where the instability-wave growth is affected by both mean-flow-divergence and nonlinear effects and is eventually converted to decay. A uniformly valid composite formula for the instability wave amplitude, accounting for both nonparallel and nonlinear effects, is given and compared to experimental results. The inviscid solutions to these equations always end in a singularity at finite downstream distance.

Hultgren, L. S.↗
NASA NTRS1992

A numerical investigation of hydrogen combustion in Mach 2 flow

A numerical study is conducted of a reacting flowfield generated by a single hydrogen jet injected transversely behind a rearward facing step. A nonreacting mixing study was followed by a reacting simulation. The computation simulates a current experimental condition. The validation of the numerical solution was limited to a comparison of the wall-pressure distribution along the wall. The comparison indicates agreement between the experiment and the prediction with a maximum error of 7 percent. The addition of the reaction responsible for HO2 production (H + O2 + M = HO2 + M) to an initially simplified chemical mechanism reduced the exponential growth of the free radicals and reduced the amount of heat released by combustion; as a result, the flowfield was significantly changed. A reversed flow was obtained in limited regions of the flow.

Segal, Corin↗
NASA NTRS1991

Subharmonic Route to Boundary-Layer Transition - Critical Layer Nonlinearity

The linear and nonlinear dynamics of a triad of initially linear stability waves comprising a single plane wave at fundamental frequency and two symmetric oblique waves with half the frequency and streamwise wave number of the plane wave are presented. Analysis is performed for the initial nonlinear development of the waves where the order of the oblique waves' amplitude is equal to or less than that of the plane wave. Results show that the fundamental basically follows the linear theory, while the subharmonic follows an exponential-of-an-exponential growth.

Mankbadi, Reda R.↗