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On velocity and reactive scalar spectra in turbulent premixed flames
AbstractKinetic energy and reactive scalar spectra in turbulent premixed flames are studied from compressible three-dimensional direct numerical simulations (DNS) of a temporally evolving rectangular slot-jet premixed flame, a statistically one-dimensional configuration. The flames correspond to a lean premixed hydrogen–air mixture at an equivalence ratio of 0.7, preheated to 700 K and at 1 atm, and three DNS are considered with a fixed jet Reynolds number of 10 000 and a jet Damköhler number varying between 0.13 and 0.54. For the study of spectra, motivated by the need to account for density change, which can be locally strong in premixed flames, a new density-weighted definition for two-point velocity/scalar correlations is proposed. The density-weighted two-point correlation tensor retains the essential properties of its constant-density (incompressible) counterpart and recovers the density-weighted Reynolds stress tensor in the limit of zero separation. The density weighting also allows the derivation of balance equations for velocity and scalar spectrum functions in the wavenumber space that illuminate physics unique to combusting flows. Pressure–dilatation correlation is a source of kinetic energy at high wavenumbers and, analogously, reaction rate–scalar fluctuation correlation is a high-wavenumber source of scalar energy. These results are verified by the spectra constructed from the DNS data. The kinetic energy spectra show a distinct inertial range with a scaling followed by a ‘diffusive–reactive’ range at higher wavenumbers. The exponential drop-off in this range shows a distinct inflection in the vicinity of the wavenumber corresponding to a laminar flame thickness, , and this is attributed to the contribution from the pressure–dilatation term in the energy balance in wavenumber space. Likewise, a clear spike in spectra of major reactant species (hydrogen) arising from the reaction-rate term is observed at wavenumbers close to . It appears that in the inertial range classical scaling laws for the spectra involving the Kolmogorov scale are applicable, but in the high-wavenumber range where chemical reactions have a strong signature the laminar flame thickness produces a better collapse. It is suggested that a full scaling should perhaps involve the Kolmogorov scale, laminar flame thickness, Damköhler number and Karlovitz number.This is the accepted manuscript. The final version is available from CUP at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9317552&fileId=S0022112014003929
Shift in the velocity of a front due to a cut-off
We consider the effect of a small cut-off epsilon on the velocity of a
traveling wave in one dimension. Simulations done over more than ten orders of
magnitude as well as a simple theoretical argument indicate that the effect of
the cut-off epsilon is to select a single velocity which converges when epsilon
tends to 0 to the one predicted by the marginal stability argument. For small
epsilon, the shift in velocity has the form K(log epsilon)^(-2) and our
prediction for the constant K agrees very well with the results of our
simulations. A very similar logarithmic shift appears in more complicated
situations, in particular in finite size effects of some microscopic stochastic
systems. Our theoretical approach can also be extended to give a simple way of
deriving the shift in position due to initial conditions in the
Fisher-Kolmogorov or similar equations.Comment: 12 pages, 3 figure
Gastrointestinal Motility in Health and Disease
Michael Zabinski (with Biancani, P., M. P. Zabinski, M. D. Kerstein, and J. Behar) is a contributing author, Comparison of mechanical characteristics of the lower oesophageal sphincter and pyloric sphincter, p.547-551.
Book description:
Proceedings of the 6th International Symposium on Gastrointestinal Motility, held at the Royal College of Surgeons of Edinburgh, 12–16th September, 1977.https://digitalcommons.fairfield.edu/engineering-books/1036/thumbnail.jp
Emergence of pulled fronts in fermionic microscopic particle models
We study the emergence and dynamics of pulled fronts described by the
Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation in the microscopic
reaction-diffusion process A + A A$ on the lattice when only a particle is
allowed per site. To this end we identify the parameter that controls the
strength of internal fluctuations in this model, namely, the number of
particles per correlated volume. When internal fluctuations are suppressed, we
explictly see the matching between the deterministic FKPP description and the
microscopic particle model.Comment: 4 pages, 4 figures. Accepted for publication in Phys. Rev. E as a
Rapid Communicatio
The Thermonuclear Explosion Of Chandrasekhar Mass White Dwarfs
The flame born in the deep interior of a white dwarf that becomes a Type Ia
supernova is subject to several instabilities. We briefly review these
instabilities and the corresponding flame acceleration. We discuss the
conditions necessary for each of the currently proposed explosion mechanisms
and the attendant uncertainties. A grid of critical masses for detonation in
the range - g cm is calculated and its
sensitivity to composition explored. Prompt detonations are physically
improbable and appear unlikely on observational grounds. Simple deflagrations
require some means of boosting the flame speed beyond what currently exists in
the literature. ``Active turbulent combustion'' and multi-point ignition are
presented as two plausible ways of doing this. A deflagration that moves at the
``Sharp-Wheeler'' speed, , is calculated in one dimension
and shows that a healthy explosion is possible in a simple deflagration if the
front moves with the speed of the fastest floating bubbles. The relevance of
the transition to the ``distributed burning regime'' is discussed for delayed
detonations. No model emerges without difficulties, but detonation in the
distributed regime is plausible, will produce intermediate mass elements, and
warrants further study.Comment: 28 pages, 4 figures included, uses aaspp4.sty. Submitted to Ap
Improved Lagrangian mixing models for passive scalars in isotropic turbulence
Lagrangian data for velocity, scalars, and energy and scalar dissipation from direct numerical simulations are used to validate Lagrangian mixing models for inert passive scalars in stationary isotropic turbulence. The scalar fluctuations are nearly Gaussian, and, as a result of production by uniform mean gradients, statistically stationary. Comparisons are made for Taylor-scale Reynolds numbers in the range 38 to about 240 and Schmidt numbers in the range 1/8 to 1. Model predictions for one-point, one-time Eulerian statistics ~Eulerian correspondence! and one-particle, two-time Lagrangian statistics ~Lagrangian correspondence! are examined. Two scalar mixing models, namely the Lagrangian Fokker–Planck model and the Lagrangian colored-noise ~LCN! model, are proposed and written in terms of stochastic differential equations ~SDE! with specified drift and diffusion terms. Both of these models rely on statistics of the scalar field conditioned upon the energy dissipation, as provided by the Lagrangian spectral relaxation ~LSR! model. With the exception of the scalar dissipation, the models are shown to capture the Reynolds and Schmidt-number dependence of the Lagrangian integral time scales. However, the LCN model provides a more realistic description of the Lagrangian scalar fluctuations as differentiable time series having the correct form of the scalar autocorrelation function. Further extensions of the new mixing models to non-Gaussian scalars are conceptually straightforward, but require a closure for the scalar-conditioned scalar dissipation rate matrix. Likewise, accurate prediction of joint statistics for differential diffusion between different scalars with unequal molecular diffusivities will require the formulation of a multiscale SDE similar to the LSR model
Non-Gaussian Distributions in Extended Dynamical Systems
We propose a novel mechanism for the origin of non-Gaussian tails in the
probability distribution functions (PDFs) of local variables in nonlinear,
diffusive, dynamical systems including passive scalars advected by chaotic
velocity fields. Intermittent fluctuations on appropriate time scales in the
amplitude of the (chaotic) noise can lead to exponential tails. We provide
numerical evidence for such behavior in deterministic, discrete-time passive
scalar models. Different possibilities for PDFs are also outlined.Comment: 12 pages and 6 figs obtainable from the authors, LaTex file,
OSU-preprint-
The role of cell-cell adhesion in wound healing
We present a stochastic model which describes fronts of cells invading a
wound. In the model cells can move, proliferate, and experience cell-cell
adhesion. We find several qualitatively different regimes of front motion and
analyze the transitions between them. Above a critical value of adhesion and
for small proliferation large isolated clusters are formed ahead of the front.
This is mapped onto the well-known ferromagnetic phase transition in the Ising
model. For large adhesion, and larger proliferation the clusters become
connected (at some fixed time). For adhesion below the critical value the
results are similar to our previous work which neglected adhesion. The results
are compared with experiments, and possible directions of future work are
proposed.Comment: to appear in Journal of Statistical Physic
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