A four-step reduced chemical-kinetic mechanism for syngas combustion is proposed for use under conditions of interest for gas-turbine operation. The mechanism builds upon our recently published three-step mechanism for H 2 -air combustion (Boivin et al., Proc. Comb. Inst. 33, 2010), which was cate that the reduced description can be applied with reasonable accuracy in numerical studies of gas-turbine syngas combustion.

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Radionuclide scanning images published inNatureby Di Chiro in 1964 showed a downward migration along the spinal canal of particle tracers injected in the brain ventricles while also showing an upward flow of tracers injected in the lumbar region of the canal. These observations, since then corroborated by many radiological measurements, have been the basis for the hypothesis that there must be an active circulation mechanism associated with the transport of cerebrospinal fluid (CSF) deep down into the spinal canal and subsequently returning a portion back to the cranial vault. However, to date, there has been no physical explanation for the mechanism responsible for the establishment of such a bulk recirculating motion. To investigate the origin and characteristics of this recirculating flow, we have analyzed the motion of the CSF in the subarachnoid space of the spinal canal. Our analysis accounts for the slender geometry of the spinal canal, the small compliance of the dura membrane enclosing the CSF in the canal, and the fact that the CSF is confined to a thin annular subarachnoid space surrounding the spinal cord. We apply this general formulation to study the characteristics of the flow generated in a simplified model of the spinal canal consisting of a slender compliant cylindrical pipe with a coaxial cylindrical inclusion, closed at its distal end, and subjected to small periodic pressure pulsations at its open entrance. We show that the balance between the local acceleration and viscous forces produces a leading-order flow consisting of pure oscillatory motion with axial velocities on the order of a few centimetres per second and amplitudes monotonically decreasing along the length of the canal. We then demonstrate that the nonlinear term associated with the convective acceleration contributes to a second-order correction consisting of a steady streaming that generates a bulk recirculating motion of the CSF along the length of the canal with characteristic velocities two orders of magnitude smaller than the leading-order oscillatory flow. The results of the analysis of this idealized geometry of the spinal canal are shown to be in good agreement not only with experimental measurements in anin-vitromodel but also with radiological measurements conducted in human adults.

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This paper investigates the transport of a solute carried by the cerebrospinal fluid (CSF) in the spinal canal. The analysis is motivated by the need for a better understanding of drug dispersion in connection with intrathecal drug delivery (ITDD), a medical procedure used for treatment of some cancers, infections and pain, involving the delivery of the drug to the central nervous system by direct injection into the CSF via the lumbar route. The description accounts for the CSF motion in the spinal canal, described in our recent publication (Sánchez et al., J. Fluid Mech., vol. 841, 2018, pp. 203–227). The Eulerian velocity field includes an oscillatory component with angular frequency $\unicode[STIX]{x1D714}$, equal to that of the cardiac cycle, and associated tidal volumes that are a factor $\unicode[STIX]{x1D700}\ll 1$ smaller than the total CSF volume in the spinal canal, with the small velocity corrections resulting from convective acceleration providing a steady-streaming component with characteristic residence times of order $\unicode[STIX]{x1D700}^{-2}\unicode[STIX]{x1D714}^{-1}\gg \unicode[STIX]{x1D714}^{-1}$. An asymptotic analysis for $\unicode[STIX]{x1D700}\ll 1$ accounting for the two time scales $\unicode[STIX]{x1D714}^{-1}$ and $\unicode[STIX]{x1D700}^{-2}\unicode[STIX]{x1D714}^{-1}$ is used to investigate the prevailing drug-dispersion mechanisms and their dependence on the solute diffusivity, measured by the Schmidt number $S$. Convective transport driven by the time-averaged Lagrangian velocity, obtained as the sum of the Eulerian steady-streaming velocity and the Stokes-drift velocity associated with the non-uniform pulsating flow, is found to be important for all values of $S$. By way of contrast, shear-enhanced Taylor dispersion, which is important for values of $S$ of order unity, is shown to be negligibly small for the large values $S\sim \unicode[STIX]{x1D700}^{-2}\gg 1$ corresponding to the molecular diffusivities of all ITDD drugs. Results for a model geometry indicate that a simplified equation derived in the intermediate limit $1\ll S\ll \unicode[STIX]{x1D700}^{-2}$ provides sufficient accuracy under most conditions, and therefore could constitute an attractive reduced model for future quantitative analyses of drug dispersion in the spinal canal. The results can be used to quantify dependences of the drug-dispersion rate on the frequency and amplitude of the pulsation of the intracranial pressure, the compliance and specific geometry of the spinal canal and the molecular diffusivity of the drug.

We present a numerical study of the spatiotemporal, inviscid linear instability of light jets emerging from round tubes for values of the Reynolds number, Re j = j Q / ͑a j ͒ ӷ 1, where Q is the volumetric flow rate, j and j are, respectively, the jet density and viscosity, and a is the injection tube radius. The analysis focuses on the influence of the injector length l t on the stability characteristics of the resulting jet, whose base velocity profile at the exit is computed in terms of the dimensionless tube length L t = l t / ͑Re j a͒ by integrating the boundary-layer equations along the injector. Both axisymmetric ͑m =0͒ and helical ͉͑m͉ =1͒ modes of instability are investigated for different values of the jet-to-ambient density ratio S = j / ϱ Ͻ 1. For short tubes L t Ӷ 1 the base velocity profile at the tube exit is uniform except in a thin surrounding boundary layer. Correspondingly, the stability analysis reproduces previous results of uniform velocity jets, according to which the jet becomes absolutely unstable to axisymmetric modes for a critical density ratio S c Ӎ 0.66 and to helical modes for S c Ӎ 0.35. For tubes of increasing length the analysis reveals that both modes exhibit absolutely unstable regions for all values of L t and small enough values of the density ratio. In the case of the helical mode, we find that S c increases monotonically with L t , reaching its maximum value S c Ӎ 0.5 as the exit velocity approaches the Poiseuille profile for L t ӷ 1. Concerning the axisymmetric mode, its associated value of S c achieves a maximum value S c Ӎ 0.9 for L t Ӎ 0.04 and then decreases to approach S c Ӎ 0.7 for L t ӷ 1. The absolute growth rates in this limiting case of near-Poiseuille jet profiles are, however, extremely small for m =0, in agreement with the fact that axisymmetric disturbances of a jet with parabolic profile are neutrally stable. As a result, for S Ͻ 0.5 the absolute growth rate of the helical mode becomes larger than that of the axisymmetric mode for sufficiently large values of L t , suggesting that the helical mode may prevail in the instability development of very light jets issuing from long injectors.

A short mechanism consisting of seven elementary reactions, of which only three are reversible, is shown to provide good predictions of hydrogen-air lean-flame burning velocities. This mechanism is further simplified by noting that over a range of conditions of practical interest, near the lean flammability limit all reaction intermediaries have small concentrations in the important thin reaction zone that controls the hydrogen-air laminar burning velocity and therefore follow a steady state approximation, while the main species react according to the global irreversible reaction 2H 2 + O 2 → 2H 2 O. An explicit expression for the non-Arrhenius rate of this one-step overall reaction for hydrogen oxidation is derived from the seven-step detailed mechanism, for application near the flammability limit. The one-step results are used to calculate flammability limits and burning velocities of planar deflagrations. Furthermore, implications concerning radical profiles in the deflagration and reasons for the success of the approximations are clarified. It is also demonstrated that adding only two irreversible direct recombination steps to the seven-step mechanism accurately reproduces burning velocities of the full detailed mechanism for all equivalence ratios at normal atmospheric conditions and that an eight-step detailed mechanism, constructed from the seven-step mechanism by adding to it the fourth reversible shuffle reaction, improves predictions of O and OH profiles. The new reduced-chemistry descriptions can be useful for both analytical and computational studies of lean hydrogen-air flames, decreasing required computation times.

This paper addresses homogeneous ignition of hydrogen-oxygen mixtures when the initial conditions of temperature and pressure place the system below the crossover temperature associated with the second explosion limit.A three-step reduced mechanism involving H 2 , O 2 , H 2 O, H 2 O 2 and HO 2 , derived previously from a skeletal mechanism of eight elementary steps by assuming O, OH and H to follow steady state, is seen to describe accurately the associated thermal explosion. At sufficiently low temperatures, HO 2 consumption through HO 2 + HO 2 → H 2 O 2 + O 2 is fast enough to place this intermediate in steady state after a short build-up period, thereby reducing further the chemistry description to the two global steps 2H 2 + O 2 → 2H 2 O and 2H 2 O → H 2 O 2 + H 2 . The strong temperature sensitivity of the corresponding overall rates enables activation-energy asymptotics to be used in describing the resulting thermal runaway, yielding an explicit expression that predicts with excellent accuracy the ignition time for different conditions of initial temperature, composition, and pressure.