A Model of Reduced Kinetics for Alkane Oxidation Using Constituents and Species for N-Heptane

The reduction of elementary or skeletal oxidation kinetics to a subgroup of tractable reactions for inclusion in turbulent combustion codes has been the subject of numerous studies. The skeletal mechanism is obtained from the elementary mechanism by removing from it reactions that are considered negligible for the intent of the specific study considered. As of now, there are many chemical reduction methodologies. A methodology for deriving a reduced kinetic mechanism for alkane oxidation is described and applied to n-heptane. The model is based on partitioning the species of the skeletal kinetic mechanism into lights, defined as those having a carbon number smaller than 3, and heavies, which are the complement of the species ensemble. For modeling purposes, the heavy species are mathematically decomposed into constituents, which are similar but not identical to groups in the group additivity theory. From analysis of the LLNL (Lawrence Livermore National Laboratory) skeletal mechanism in conjunction with CHEMKIN II, it is shown that a similarity variable can be formed such that the appropriately non-dimensionalized global constituent molar density exhibits a self-similar behavior over a very wide range of equivalence ratios, initial pressures and initial temperatures that is of interest for predicting n-heptane oxidation. Furthermore, the oxygen and water molar densities are shown to display a quasi-linear behavior with respect to the similarity variable. The light species ensemble is partitioned into quasi-steady and unsteady species. The reduced model is based on concepts consistent with those of Large Eddy Simulation (LES) in which functional forms are used to replace the small scales eliminated through filtering of the governing equations; in LES, these small scales are unimportant as far as the overwhelming part of dynamic energy is concerned. Here, the scales thought unimportant for recovering the thermodynamic energy are removed. The concept is tested by using tabular information from the LLNL skeletal mechanism in conjunction with CHEMKIN II utilized as surrogate ideal functions replacing the necessary functional forms. The test reveals that the similarity concept is indeed justified and that the combustion temperature is well predicted, but that the ignition time is over-predicted, a fact traced to neglecting a detailed description of the processes leading to the heavies chemical decomposition. To palliate this deficiency, functional modeling is incorporated into this conceptual reduction in addition to the modeling the evolution of the global constituent molar density, the enthalpy evolution of the heavies, the contribution to the reaction rate of the unsteady lights from other light species and from the heavies, the molar density evolution of oxygen and water, and the mole fractions of the quasisteady light species. The model is compact in that there are only nine species-related progress variables. Results are presented showing the performance of the model for predicting the temperature and species evolution. The model reproduces the ignition time over a wide range of equivalence ratios, initial pressure, and initial temperature

Modelling of subgrid-scale phenomena in supercritical transitional mixing layers: an a priori study

A database of transitional direct numerical simulation (DNS) realizations of a supercritical mixing layer is analysed for understanding small-scale behaviour and examining subgrid-scale (SGS) models duplicating that behaviour. Initially, the mixing layer contains a single chemical species in each of the two streams, and a perturbation promotes roll-up and a double pairing of the four spanwise vortices initially present. The database encompasses three combinations of chemical species, several perturbation wavelengths and amplitudes, and several initial Reynolds numbers specifically chosen for the sole purpose of achieving transition. The DNS equations are the Navier-Stokes, total energy and species equations coupled to a real-gas equation of state; the fluxes of species and heat include the Soret and Dufour effects. The large-eddy simulation (LES) equations are derived from the DNS ones through filtering. Compared to the DNS equations, two types of additional terms are identified in the LES equations: SGS fluxes and other terms for which either assumptions or models are necessary. The magnitude of all terms in the LES conservation equations is analysed on the DNS database, with special attention to terms that could possibly be neglected. It is shown that in contrast to atmospheric-pressure gaseous flows, there are two new terms that must be modelled: one in each of the momentum and the energy equations. These new terms can be thought to result from the filtering of the nonlinear equation of state, and are associated with regions of high density-gradient magnitude both found in DNS and observed experimentally in fully turbulent high-pressure flows. A model is derived for the momentum-equation additional term that performs well at small filter size but deteriorates as the filter size increases, highlighting the necessity of ensuring appropriate grid resolution in LES. Modelling approaches for the energy-equation additional term are proposed, all of which may be too computationally intensive in LES. Several SGS flux models are tested on an a priori basis. The Smagorinsky (SM) model has a poor correlation with the data, while the gradient (GR) and scale-similarity (SS) models have high correlations. Calibrated model coefficients for the GR and SS models yield good agreement with the SGS fluxes, although statistically, the coefficients are not valid over all realizations. The GR model is also tested for the variances entering the calculation of the new terms in the momentum and energy equations; high correlations are obtained, although the calibrated coefficients are not statistically significant over the entire database at fixed filter size. As a manifestation of the small-scale supercritical mixing peculiarities, both scalar-dissipation visualizations and the scalar-dissipation probability density functions (PDF) are examined. The PDF is shown to exhibit minor peaks, with particular significance for those at larger scalar dissipation values than the mean, thus significantly departing from the Gaussian behaviour

Quantum state preparation and macroscopic entanglement in gravitational-wave detectors

Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the new possibility of experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical behavior of objects in the realm of everyday experience - using gravitational-wave detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometer's classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the classical noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum state preparation, and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses, and the performance of the planned Advanced LIGO interferometers in quantum-state preparation

Searching for stochastic gravitational waves using data from the two colocated LIGO Hanford detectors

Searches for a stochastic gravitational-wave background (SGWB) using terrestrial detectors typically involve cross-correlating data from pairs of detectors. The sensitivity of such cross-correlation analyses depends, among other things, on the separation between the two detectors: the smaller the separation, the better the sensitivity. Hence, a colocated detector pair is more sensitive to a gravitational-wave background than a noncolocated detector pair. However, colocated detectors are also expected to suffer from correlated noise from instrumental and environmental effects that could contaminate the measurement of the background. Hence, methods to identify and mitigate the effects of correlated noise are necessary to achieve the potential increase in sensitivity of colocated detectors. Here we report on the first SGWB analysis using the two LIGO Hanford detectors and address the complications arising from correlated environmental noise. We apply correlated noise identification and mitigation techniques to data taken by the two LIGO Hanford detectors, H1 and H2, during LIGO’s fifth science run. At low frequencies, 40–460 Hz, we are unable to sufficiently mitigate the correlated noise to a level where we may confidently measure or bound the stochastic gravitational-wave signal. However, at high frequencies, 460–1000 Hz, these techniques are sufficient to set a 95% confidence level upper limit on the gravitational-wave energy density of Ω(f) < 7.7 × 10[superscript -4](f/900  Hz)[superscript 3], which improves on the previous upper limit by a factor of ~180. In doing so, we demonstrate techniques that will be useful for future searches using advanced detectors, where correlated noise (e.g., from global magnetic fields) may affect even widely separated detectors.National Science Foundation (U.S.)United States. National Aeronautics and Space AdministrationCarnegie TrustDavid & Lucile Packard FoundationAlfred P. Sloan Foundatio

Alkane Kinetics Reduction Consistent with Turbulence Modeling using Large Eddy Simulation

A methodology for deriving a reduced kinetic mechanism for alkane oxidation is described, inspired by n-heptane oxidation. The model is based on partitioning the species of the skeletal kinetic mechanism into lights, defined as those having a carbon number smaller than 3, and heavies, which are the complement of the species ensemble. For modeling purposes, the heavy species are mathematically decomposed into constituents, which are similar but not identical to groups in the group additivity theory. From analysis of the n-heptane LLNL skeletal mechanism in conjunction with CHEMKIN II, it is shown that a similarity variable can be formed such that the appropriately non-dimensionalized global constituent molar density exhibits a self-similar behavior over a very wide range of equivalence ratios, initial pressures and initial temperatures that is of interest for predicting n-heptane oxidation. Furthermore, the oxygen and water molar densities are shown to display a quasi-linear behavior with respect to the similarity variable. The light species ensemble is partitioned into quasi-steady and unsteady species. The reduced model is based on concepts consistent with those of Large Eddy Simulation in which functional forms are used to replace the small scales eliminated through Altering of the governing equations; these small scales are unimportant as far as dynamic energy is concerned. Here, we remove the scales deemed unimportant for recovering the thermodynamic energy. The concept is tested by using tabular information from the n-heptane LLNL skeletal mechanism in conjunction with CHEMKIN II utilized as surrogate ideal functions replacing the necessary functional forms. The test reveals that the similarity concept is indeed justified and that the combustion temperature is well predicted, but that the ignition time is overpredicted, which is traced to neglecting a detailed description of the processes lending to the heavies chemical decomposition. To palliate this deficiency, functional modeling is incorporated into our conceptual reduction. This functional modeling includes the global constituent molar density, the enthalpy evolution of the heavies, the contribution to the reaction rate of the unsteady lights from other light species and from the heavies, the molar density evolution of oxygen and water, and the mole &actions of the quasi-steady light species. The model is compact in that there are only nine species-related progress variables. Results are presented showing the performance of the model for predicting the temperature and species evolution for n-heptane. The model reproduces the ignition time over a wide range of equivalence ratios, initial pressure and initial temperature. Preliminary results for iso-octane using the full mechanism are also presented, showing encouragingly that the concept may be generalized to other alkanes. The utility of the model and possible improvements are discussed

Computation of Laminar Premixed Flames Using Reduced Kinetics Based on Constituents and Species

A model is proposed for quasi-one-dimensional steady flame development in the configuration of an inviscid, premixed fuel jet injected into air. The governing equations are written within the framework of a reduced kinetic model based on constituents and species. The reduced kinetic model, previously exercised in a constant-volume perfectly-stirred reactor mode, has been successful at predicting ignition and combustion product and temperature evolution for n-heptane, iso-octane, PRF fuel combinations, and mixtures of iso-octane with either n-pentane or iso-hexane. The differential governing equations have the option of an axially variable area and they are coupled with a real gas equation of state. The flame development model accounts for a full diffusion matrix, and thermal conductivity computed for the species mixture. Preliminary results are presented