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A discrete finite dimensional system, nonharmonic Fourier series and controllability, reduction to canonical form, and spectral synthesis are considered. The extent to which the eigenvalue associated with a controllable pair of a certain type may be modified via continuous linear state feedback is demonstrated.
A time-independent convection diffusion equation is studied by means of a compact finite difference scheme and numerical solutions are compared to the analytic inviscid solutions. The correct internal and external boundary layer behavior is observed, due to an inherent feature of the scheme which automatically produces upwind differencing in inviscid regions and the correct viscous behavior in viscous regions.
A discrete finite dimensional system, nonharmonic Fourier series and controllability, reduction to canonical form, and spectral synthesis are considered. The extent to which the eigenvalue associated with a controllable pair of a certain type may be modified via continuous linear state feedback is demonstrated. Previously announced in STAR as N83-28925
A time-independent convection diffusin equation is studied by means of a compact finite difference scheme and numerical solutions are compared to the analytic inviscid solutions. The correct internal and external boundary layer behavior is observed, due to an inherent feature of the scheme which automatically produces upwind differencing in inviscid regions and the correct viscous behavior in viscous regions.
Combustor models for the aircraft gas turbine industry have been obtained because of the need to reduce the costs of developing improved performance and more durable engines. A few years ago, it became apparent that the mass concentration and velocity predictions provided by the computer codes were not representing the data measured in some confined recirculating flows. It is pointed out that errors in the mass concentration distribution are an especially serious problem because of their influence on the heat release, temperature, and reactant distributions. Combined mass and momentum turbulent transport experiments with swirling and nonswirling flow have been conducted with the objective to obtain an experimental data base which can be used to evaluate and improve the turbulent transport submodes employed in the aerothermal models. The present paper is mainly concerned with the overall characteristics of the mass turbulent transport processes in complex flows with recirculation and the deficiencies of the conventional models.
Performance tests of the third-order turbulence closure for predictions of separating and recirculating flows in backward-facing steps were studied. Computations of the momentum and temperature fields in the flow domain being considered entail the solution of time-averaged transport equations containing the second-order turbulent fluctuating products. The triple products, which are responsible for the diffusive transport of the second-order products, attain greater significance in separating and reattaching flows. The computations are compared with several algebraic models and with the experimental data. The prediction was improved considerably, particularly in the separated shear layer. Computations are further made for the temperature-velocity double products and triple products. Finally, several advantages were observed in the usage of the transport equations for the evaluation of the turbulence triple products; one of the most important features is that the transport model can always take the effects of convection and diffusion into account in strong convective shear flows such as reattaching separated layers while conventional algebraic models cannot account for these effects in the evaluation of turbulence variables.
The only atomic or molecular spectra known to exhibit 'collisional interference' effects are those of H2 and its isotopes. Attention is presently given to the sharp absorption spectra of HD, which demonstrate collisional interference effects is a fashion that while surprising has been experimentally verified and theoretically characterized in detail. Collisional interference can dramatically alter the line shapes usually encountered in dipole absorption spectra, while nevertheless remaining narrow.
Relativistic p-Ca-40 elastic scattering observables are calculated using relativistic NN amplitudes obtained from the solution of a two-body relativistic equation in which one particle is kept on its mass-shell. Results at 200 MeV are presented for two sets of NN amplitudes, one with pure pseudo-vector coupling for the pion and another with a 25 percent admixture of pseudo-scaling coupling. Both give a very good fit to the positive energy on-shell NN data. Differences between the predictions of these two models (which are shown to be due only to the differences in their corresponding negative energy amplitudes) provide a measure of the uncertainty in contructing Dirac optical potentials from NN amplitudes.
The author shows that the sum or difference of two vectors is a vector. Similarly the sum of any two tensors of the same order is a tensor of that order. No meaning is attached to the sum of tensors of different orders, say u(sub i) + u(sub ij); that is not a tensor. In general, an equation containing tensors has meaning only if all the terms in the equation are tensors of the same order, and if the same unrepeated subscripts appear in all the terms. These facts will be used in obtaining appropriate equations for fluid turbulence. With the foregoing background, the derivation of appropriate continuum equations for turbulence should be straightforward.
Estimates of the location and extension of the upwind ground area that affects flux observations most directly are examined to determine the reliability of airborne versus near-ground flux measurements. The theoretical issues regarding the 'footprint' are examined, and specific observations are analyzed by studying the data over a grid regarding sensible heat, latent heat, CO2, and greenness. The grid is footprint-corrected to correlate better with independently observed surface characteristics, and an optimized footprint is developed that satisfies the relationships between the observed variables. Optimized mapping of the surface flux is given which demonstrates the importance of considering local advection to correlate airborne and ground-based flux observations. The technique is particularly applicable to situations in which significant variations in the surface flux density exist.
An experimental correlation is derived for gas absorption at a turbulent, shear-free liquid interface. The correlation is expressed in terms of the liquid-side turbulence intensity, liquid-side macroscale, and the properties of the diffusing gas and solvent. The transfer coefficient increases linearly with rms velocity up to a point where the eddy Reynolds number reaches a critical (Schmidt number dependent) value. At higher velocities, there is a more rapid linear rise. The slope of the lower Reynolds number region is proportional to the square root of the diffusivity; at Reynolds numbers much higher than that of the break point, the slope becomes independent of diffusivity.
A thermal NO(x) prediction model is developed to interface with a CFD, k-epsilon based code. A converged solution from the CFD code is the input to the postprocessing model for prediction of thermal NO(x). The model uses a decoupled analysis to estimate the equilibrium level of (NO(x))e which is the constant rate limit. This value is used to estimate the flame (NO(x)) and in turn predict the rate of formation at each node using a two-step Zeldovich mechanism. The rate is fixed on the NO(x) production rate plot by estimating the time to reach equilibrium by a differential analysis based on the reaction: O + N2 = NO + N. The rate is integrated in the nonequilibrium time space based on the residence time at each node in the computational domain. The sum of all nodal predictions yields the total NO(x) level.
The probability density function (PDF) method has been proven a very useful approach in turbulence research. It has been particularly effective in simulating turbulent reacting flows and in studying some detailed statistical properties generated by a turbulent field There are, however, some important questions that have yet to be answered in PDF studies. Our efforts in the past year have been focused on two areas. First, a simple mixing model suitable for Monte Carlo simulations has been developed based on the mapping closure. Secondly, the mechanism of turbulent transport has been analyzed in order to understand the recently observed abnormal PDF's of turbulent temperature fields generated by linear heat sources.
Unseeded molecular tagging methods based on single-photon processes that produce long tag lines (>50 mm) have been recently developed and demonstrated by the Combustion Laser Diagnostics Group (Mechanical Engineering Department) at Vanderbilt University [1,2]. In Ozone Tagging Velocimetry (OTV) a line of ozone (O3) is produced by a single photon from a pulsed narrowband argon fluoride (ArF) excimer laser operating at - 193 nm. After a known time delay, t, the position of the displaced (convected in the flow field) O3 tag line is revealed by photodissociation of O3 and subsequent fluorescence of O2, caused by a pulsed laser sheet from a krypton fluoride (KrF) excimer laser operating at - 248 nm. Intensified CCD camera images of the fluorescence are taken from the initial and final tag line locations thus providing unobtrusive means of establishing a velocity profile in the interrogated flow field. The O3 lines are "written" and subsequently "read" by the following reactions:
A new method of estimating temperatures and gas species concentrations (CO2 and H2O) in a laminar flame is reported. The path-integrated, spectral radiation intensities emitted from a laminar flame at multiple wavelengths and view angles are calculated using a narrow band radiation model. Synthetic data, in the form of radial profiles of temperature and gas concentrations, are used in these calculations. The calculations mimic measurements that would theoretically be obtained using a mid-infrared spectrometer with a scanner. The path integrated spectral radiation intensities are deconvoluted using a maximum likelihood estimation method in conjunction with an iterative scheme. The deconvolution algorithm accounts for the self-absorption of radiation by the intervening gases, and provides the local temperature and gas species concentrations. The deconvoluted temperatures and gas concentrations are compared with the synthetic data used for calculating the spectral radiation intensities. The deconvoluted temperatures and gas species concentrations are within 0.5 % of the synthetic data. The deconvolution algorithm is expected to provide combustion researchers with an easy method of obtaining the radial profiles of major gas species concentrations and temperatures in laminar flames non-intrusively using a mid-infrared spectrometer with a scanner.
EUPDF-II provides the solution for the species and temperature fields based on an evolution equation for PDF (Probability Density Function) and it is developed mainly for application with sprays, combustion, parallel computing, and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase CFD and spray solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type. The manual provides the user with an understanding of the various models involved in the PDF formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. The source code of EUPDF-II will be available with National Combustion Code (NCC) as a complete package.
Recent experiments have shown that low-density gas jets injected into a high-density gas undergo an instability mode leading to highly periodic oscillations in the flow field. The transition from laminar to turbulent flow in these jets is abrupt, without a gradual change in scales. Although this type of instability at high Richardson numbers has been attributed to buoyancy, direct physical evidence was not acquired through experiments. In this study, several experiments were conducted in Earth gravity and microgravity to acquire qualitative data on near field flow structure of helium jets injected into air. Microgravity conditions were simulated in the 2.2-second drop tower at NASA Glenn Research Center. The operating parameters of this study included the tube inside diameter, the jet Reynolds number, and the jet Richardson number. Tubes with inside diameters of 19.05 mm and 31.75 mm were used in the experiments conducted in the drop tower. The jet flow was analyzed using quantitative rainbow schlieren deflectometry, a non-intrusive line of sight measurement technique for the whole field. The flow structure was characterized by distributions of angular deflection and the resulting helium mole fraction obtained from color schlieren images taken at 60 Hz. Three sets of experimental data with respect to three schlieren fields of view were acquired for each tube. Results show that the jet in microgravity was up to 70 percent wider than that in Earth gravity. The global jet flow oscillations observed in Earth gravity were absent in microgravity, providing direct experimental evidence that the flow instability in the low-density jet was buoyancy-induced. This study provides quantitative details of temporal flow evolution as the experiments undergo change in gravity in the drop tower.
The flow structure of a pulsating helium jet was investigated using quantitative rainbow schlieren deflectometry. The operating parameters included the tube inside diameter, the jet Reynolds number and the jet Richardson number. The jet structure was characterized by the frequency spectrum, temporal evolution of the oscillations and mean and root-mean-square profiles of the species mole fraction, which in this case, was helium. Experiments were conducted using a variable nozzle facility. Angular deflection data were obtained using rainbow schlieren deflectometry across full field of color images taken at a temporal resolution of 60Hz. The flicker cycle was analyzed by instantaneous rainbow schlieren images, contour plots of deflection angle and helium mole fraction placed sequentially in time. Two observe the flow downstream, the tube was lowered with respect to the optical setup and images were taken at different axial planes. In this way, the laminar, transition and turbulent regions of the jet flow were observed. Abel inversion algorithm was utilized to reconstruct the refractive index field from the measurements of the beam deflection angle. The concentration field was then generated from the refractive index field. The phenomenon of vortex initiation and propagation in the flicker cycle was described by correlating the ray deflection angle and concentration contour plots. Experiments in the flickering jet reveal global oscillation in the flow field. The effect of jet exit Reynolds number and jet Richardson number on the flickering frequency was analyzed. The effect of jet Richardson number was more pronounced than that of the jet exit Reynolds number. The flow field was studies quantitatively in terms of temporal evolution and statistical description of helium mole fraction.