Flow field measurements of a series of turbulent premixed and stratified methane/air flames

This paper presents flow field measurements for the turbulent stratified burner introduced in two previous publications in which high resolution scalar measurements were made by Sweeney et al. [1,2] for model validation. The flow fields of the series of premixed and stratified methane/air flames are investigated under turbulent, globally lean conditions (φg=0.75). Velocity data acquired with laser Doppler anemometry (LDA) and particle image velocimetry (PIV) are presented and discussed. Pairwise 2-component LDA measurements provide profiles of axial velocity, radial velocity, tangential velocity and corresponding fluctuating velocities. The LDA measurements of axial and tangential velocities enable the swirl number to be evaluated and the degree of swirl characterized. Power spectral density and autocorrelation functions derived from the LDA data acquired at 10kHz are optimized to calculate the integral time scales. Flow patterns are obtained using a 2-component PIV system operated at 7Hz. Velocity profiles and spatial correlations derived from the PIV and LDA measurements are shown to be in very good agreement, thus offering 3D mapping of the velocities. A strong correlation was observed between the shape of the recirculation zones above the central bluff body and the effects of heat release, stoichiometry and swirl. Detailed analyses of the LDA data further demonstrate that the flow behavior changes significantly with the levels of swirl and stratification, which combines the contributions of dilatation, recirculation and swirl. Key turbulence parameters are derived from the total velocity components, combining axial, radial and tangential velocities. © 2013 The Combustion Institute.

Turbulence in Rotating, Stratified and Electrically Conducting Fluids

This book investigates how turbulence responds to rotation, stratification or magnetic fields, identifying common themes, where they exist, as well as the essential differences which inevitably arise between different classes of flow.

The evolution of a stratified turbulent cloud

Localized regions of turbulence, or turbulent clouds, in a stratified fluid are the subject of this study, which focuses on the edge dynamics occurring between the turbulence and the surrounding quiescent region. Through laboratory experiments and numerical simulations of stratified turbulent clouds, we confirm that the edge dynamics can be subdivided into materially driven intrusions and horizontally travelling internal wave-packets. Three-dimensional visualizations show that the internal gravity wave-packets are in fact large-scale pancake structures that grow out of the turbulent cloud into the adjacent quiescent region. The wave-packets were tracked in time, and it is found that their speed obeys the group speed relation for linear internal gravity waves. The energetics of the propagating waves, which include waveforms that are inclined with respect to the horizontal, are also considered and it is found that, after a period of two eddy turnover times, the internal gravity waves carry up to 16 % of the cloud kinetic energy into the initially quiescent region. Turbulent events in nature are often in the form of decaying turbulent clouds, and it is therefore suggested that internal gravity waves radiated from an initial cloud could play a significant role in the reorganization of energy and momentum in the atmosphere and oceans.©2013 Cambridge University Press.

Laminar propagation of lean premixed flames ignited in stratified mixture

Combustion in stratified mixtures is envisaged in practical energy systems such as direct-injection spark-ignited (DISI) car engines, gas turbines, for reducing CO2 and pollutant emissions while protecting their efficiency. The mixture gradients change the fundamental properties of the flame, especially by a difference in temperature and composition between the burnt gases and those of a flame consuming a homogeneous mixture. This paper presents an investigation of the properties of the flame propagating in a lean homogeneous mixture after ignition in a richer mixture according to the magnitude of the stratification. Three magnitudes of stratification are investigated. The local flame burning velocity is determined by an original PIV algorithm developed previously. The local equivalence ratio in the fresh gases is measured from anisole PLIF. From the simultaneous PIV-PLIF measurements, the flame burning velocities conditioned on the local stretch rate and equivalence ratio in fresh gases are measured. The flame propagating through the homogeneous lean mixture has properties depending on the ignition conditions in the stratified layer. The flame propagating in the lean mixture is back-supported longer for ignition under the richer condition. The change of stretch sensitivity and burning velocity of the flame in the lean mixture is measured over time for the three magnitudes of mixture stratification investigated. The ignition in richer mixtures compensates for the nonequidiffusion effect of lean propane flame and sustains its robustness to stretch. The flame propagation in the lean homogeneous mixture is enhanced by ignition in a richer stratified layer, as much by their robustness to stretch as by an increase in the flame speed or the burning velocity. The decay time of this influence of the stratification, called memory effect, is determined. © 2013 The Combustion Institute.

automatic construction of finite algebras

This paper deals withmodel generation for equational theories, i.e., automatically generating (finite) models of a given set of (logical) equations. Our method of finite model generation and a tool for automatic construction of finite algebras is described. Some examples are given to show the applications of our program. We argue that, the combination of model generators and theorem provers enables us to get a better understanding of logical theories. A brief comparison between our tool and other similar tools is also presented.

constructing finite algebras with falcon

The generation of models and counterexamples is an important form of reasoning. In this paper, we give a formal account of a system, called FALCON, for constructing finite algebras from given equational axioms. The abstract algorithms, as well as some implementation details and sample applications, are presented. The generation of finite models is viewed as a constraint satisfaction problem, with ground instances of the axioms as constraints. One feature of the system is that it employs a very simple technique, called the least number heuristic, to eliminate isomorphic (partial) models, thus reducing the size of the search space. The correctness of the heuristic is proved. Some experimental data are given to show the performance and applications of the system.

Analysis of current induced by long internal solitary waves in stratified ocean

An approximate theoretical expression for the current induced by long internal solitary waves is presented when the ocean is continuously or two-layer stratified. Particular attention is paid to characterizing velocity fields in terms of magnitude, flow components, and their temporal evolution/spatial distribution. For the two-layer case, the effects of the upper/lower layer depths and the relative layer density difference upon the induced current are further studied. The results show that the horizontal components are basically uniform in each layer with a shear at the interface. In contrast, the vertical counterparts vary monotonically in the direction of the water depth in each layer while they change sign across the interface or when the wave peak passes through. In addition, though the vertical components are generally one order of magnitude smaller than the horizontal ones, they can never be neglected in predicting the heave response of floating platforms in gravitationally neutral balance. Comparisons are made between the partial theoretical results and the observational field data. Future research directions regarding the internal wave induced flow field are also indicated.

Third-order Stokes wave solutions for interfacial internal waves in a three-layer density-stratified fluid

Interfacial internal waves in a three-layer density-stratified fluid are investigated using a singular method, and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. as expected, the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves. The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.

Second-order Stokes solutions for internal waves in three-layer density-stratified fluid

In this paper, internal waves in three-layer stratified fluid are investigated by using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. As expected, the first-order solutions are consistent with ordinary linear theoretical results, and the second-order solutions describe the second-order modification on the linear theory and the interactions between the two interfacial waves. Both the first-order and second-order solutions derived depend on the depths and densities of the three-layer fluid. It is also noted that the solutions obtained from the present work include the theoretical results derived by Umeyama as special cases.

Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random inter facial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order a symptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen (2006) as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song (2005) for second-order solutions for random interfacial waves with steady uniform currents if N=2.

Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

PROPAGATION OF SONIC BOOMS THROUGH A REAL, STRATIFIED ATMOSPHERE

Sonic boom propagation in a quiet) stratified) lossy atmosphere is the subject of this dissertation. Two questions are considered in detail: (1) Does waveform freezing occur? (2) Are sonic booms shocks in steady state? Both assumptions have been invoked in the past to predict sonic boom waveforms at the ground. A very general form of the Burgers equation is derived and used as the model for the problem. The derivation begins with the basic conservation equations. The effects of nonlinearity) attenuation and dispersion due to multiple relaxations) viscosity) and heat conduction) geometrical spreading) and stratification of the medium are included. When the absorption and dispersion terms are neglected) an analytical solution is available. The analytical solution is used to answer the first question. Geometrical spreading and stratification of the medium are found to slow down the nonlinear distortion of finite-amplitude waves. In certain cases the distortion reaches an absolute limit) a phenomenon called waveform freezing. Judging by the maturity of the distortion mechanism, sonic booms generated by aircraft at 18 km altitude are not frozen when they reach the ground. On the other hand, judging by the approach of the waveform to its asymptotic shape, N waves generated by aircraft at 18 km altitude are frozen when they reach the ground. To answer the second question we solve the full Burgers equation and for this purpose develop a new computer code, THOR. The code is based on an algorithm by Lee and Hamilton (J. Acoust. Soc. Am. 97, 906-917, 1995) and has the novel feature that all its calculations are done in the time domain, including absorption and dispersion. Results from the code compare very well with analytical solutions. In a NASA exercise to compare sonic boom computer programs, THOR gave results that agree well with those of other participants and ran faster. We show that sonic booms are not steady state waves because they travel through a varying medium, suffer spreading, and fail to approximate step shocks closely enough. Although developed to predict sonic boom propagation, THOR can solve other problems for which the extended Burgers equation is a good propagation model.