The Hydrogen Laminar Jet

Numerical and asymptotic methods are used to investigate the structure of the hydrogen jet discharging into a quiescent air atmosphere. The analysis accounts in particular for the variation of the density and transport properties with composition. The Reynolds number of the flow "Rj", based on the initial jet radius "a", the density and viscosity of the jet and the characteristic jet velocity, is assumed to take moderately large values, so that the jet remains slender and stable, and can be correspondingly described by numerical integration of the continuity, momentum and species conservation equations written in the boundary-layer approximation. The solution for the velocity and composition in the jet-development region of planar and round jets, corresponding to streamwise distances of order "Rj a", is computed numerically, along with the solutions that emerge both in the near field and in the far field. The small value of the hydrogen-to-airmolecular weight ratio is used to simplify the solution by considering the asymptotic limit of vanishing jet density. The development provides at leading order explicit analytical expressions for the far-field velocity and hydrogen mass fraction that describe accurately the hydrogen jet near the axis. The information provided can be useful in particular to characterize hydrogen discharge processes from holes and cracks.This work was supported by the SpanishMICINN under Project # ENE2008-06515-C04 and by the Comunidad de Madrid under Project S2009/ENE-1597 (HYSYCOMB)Publicad

Regimes of boundary-layer ignition by heat release from a localized energy source

This paper investigates the initiation of a deflagration in a premixed boundary-layer stream by continuous heat deposition from a line energy source placed perpendicular to the flow on the wall surface, a planar flow configuration relevant for small-scale combustion applications, including portable rotary engines. Ignition is investigated in the constant density approximation with a one-step irreversible reaction with large activation energy adopted for the chemistry description. The ratio of the characteristic strain time, given by the inverse of the wall velocity gradient, to the characteristic deflagration residence time defines the relevant controlling Damkhler number D. The time-dependent evolution following the activation of the heat source is obtained by numerical integration of the energy and fuel conservation equations. For sufficiently small values of D, the solution evolves towards a steady flow in which the chemical reaction remains confined to a finite nearsource reactive kernel. This becomes increasingly slender for increasing values of D, corresponding to smaller near-wall velocities, until a critical value D(c)1 is reached at which the confined kernel is replaced by a steady anchored deflagration, assisted by the source heating rate, which develops indefinitely downstream. As the boundary-layer velocity gradient is further decreased, a second critical Damkhler number D-c2 > D-c1 is reached at which the energy deposition results in a flashback deflagration propagating upstream against the incoming flow along the base of the boundary layer. The computations investigate the dependence of D-c1 and D-c2 on the fuel diffusivity and the dependence of D(c 1)on the source heating rate, delineating the boundaries that define the relevant regime diagram for these combustion systems.This work was supported by the Spanish MCINN through projects #CSD2010-00011, ENE2012-33213 and ENE2015-65852-C2-1-R

Reduced kinetic mechanisms for modelling LPP combustión in gas turbines

Reduced kinetic mechanisms for modelling LPP combustión in gas turbine

Laminar gas jets in high-temperature atmospheres

Numerical and asymptotic methods are used to describe the structure of low-temperature laminar gas jets discharging into a hot atmosphere of the same gas in the limit of small jet-to-ambient temperature ratios " = Tj/To 1. In the limit " ! 0, heat conduction cannot modify significantly the temperature in the cold gas, leading to a two-region flow structure consisting of a neatly defined unperturbed cold jet for r < rf (x), where T = T0/To = " and u = U0/Uj = 1, surrounded by a hot gas. These two region are separated by a transition layer where T − " " and 1 − u 1. In planar jets the front thickens with distance achieving thickness of order unity at axial distances x "−(1+)Rea forcing the near-axis fluid to change slowly its velocity and temperature, being necessary distances x "−2Rea to reach values of T and 1−u of order unity. In round jets the front remains at r = a up to distances x "−(1−)(log "−1)2 where the front is forced to move radially towards the axis of the jet, reaching r = 0 at x "−1 log "−1Rea. The arrival of the front forces the change of the velocity and temperature in the near-axis region, reaching values of order unity in a far field region of characteristic length x "−1 log "−1Rea, distance comparable to that needed by the front to achieve the axis. In both geometries, the distance necessary for the fully development of the cold jet is considerably longer than that required by the isothermal jet x Rea

Fronts in high-temperature laminar gas jets

This paper addresses the slender laminar flow resulting from the discharge of a low-Mach-number hot gas jet of radius a and moderately large Reynolds number Rj into a cold atmosphere of the same gas. We give the boundary-layer solution for plane and round jets with very small values of the ambient-to-jet temperature ratio ε accounting for the temperature dependence of the viscosity and conductivity typical of real gases. It is seen that the leading-order description of the jet in the limit ε → 0 exhibits a front-like structure, including a precisely defined separating boundary at which heat conduction and viscous shear stresses vanish in the first approximation, so that the temperature and axial velocity remain unperturbed outside the jet. Separate analyses are given for the jet discharging into a stagnant atmosphere, when the jet boundary is a conductive front, and for the jet discharging into a coflowing stream, when the jet boundary appears as a contact surface. We provide in particular the numerical description of the jet development region corresponding to axial distances of order Rja for buoyant and non-buoyant jets, as well as the self-similar solutions that emerge both in the near field and in the far field. In all cases considered, comparisons with numerical integrations of the boundary-layer problem for moderately small values of ε indicate that these front descriptions give excellent predictions for the temperature and velocity fields in the near-axis region

Laminar mixing in diluted and undiluted fuel jets upstream from lifted flames

The boundary-layer approximation is used to describe the frozen mixing process taking place when a fuel jet of radius a discharges into stagnant air. The results are applicable to the calculation of lifted flames stabilized in round laminar jets with relatively large Reynolds numbers, Re, for which the proposed formulation provides a detailed description for the velocity and composition fields encountered by the propagating triple flame formed at the base of the lifted flame. The problem is integrated for relevant values of the flow parameters, including values of the stoichiometric air-to-fuel mass ratio S of order unity, when the lifted flame is located in the region of jet development, corresponding to distances from the injector of order Re a. Further attention is given to the relevant case S ≫ 1, corresponding to typical conditions of undilute hydrocarbon-air flames, for which the resulting lifted flames are stabilized at relatively large distances from the injector, of order S Re a. It is seen that Schlichting asymptotic solution, which corresponds to a point source of momentum, is then applicable to describe the mixing process upstream from the lifted flame. Improved accuracy is sought by introducing expansions for the velocity components and for the reactant mass fractions in powers of S-1. The resulting development shows in particular that the first-order correction to the leading-order solution is equivalent to the introduction of a virtual origin for the axial coordinate. It is shown that the magnitude of the required translation, which is equal for the velocity and composition fields, must be determined from continuity considerations. As an illustrative example, the resulting description is used to calculate flame fronts with S ≫ 1 in the thermal-diffusive approximation

Confined swirling jets with large expansion ratios

This paper presents the extension of our previous investigation of confined round jets with large Reynolds numbers and large expansion ratios (Revuelta, Sanchez & Linan 2002a) to the case of swirling jets with swirl numbers of order unity. In the absence of vortex breakdown, we encounter the four-region asymptotic structure identified earlier for the non-swirling jet, including a region of jet development where the azimuthal and axial velocity components are comparable. For the flow in the long recirculating eddy that forms downstream, where the pressure differences associated with the azimuthal motion become negligible, the jet is found to act as a point source with momentum flux equal to the flow force of the incoming jet, and angular momentum flux equal to that of the jet at the orifice. The solution for the weak circulation in this slender region, including the parameter-free leading-order description and the first-order corrections, is determined by integrating the azimuthal component of the momentum equation written in the boundary-layer approximation. The results are validated through comparisons with numerical integrations of the steady axisymmetric Navier-Stokes equations, which are also used to evaluate critical conditions for vortex breakdow

Variable-density jet flows induced by concentrated sources of momentum and energy

The planar and axisymmetric variable-density flows induced in a quiescent gas by a concentrated source of momentum that is simultaneously either a source or a sink of energy are investigated for application to the description of the velocity and temperature far fields in laminar gaseous jets with either large or small values of the initial jet-to-ambient temperature ratio. The source fluxes of momentum and heat are used to construct the characteristic scales of velocity and length in the region where the density differences are of the order of the ambient density, which is slender for the large values of the Reynolds number considered herein. The problem reduces to the integration of the dimensionless boundary-layer conservation equations, giving a solution that depends on the gas transport properties but is otherwise free of parameters. The boundary conditions at the jet exit for integration are obtained by analysing the self-similar flow that appears near the heat source in planar and axisymmetric configurations and also near the heat sink in the planar case. Numerical integrations of the boundary-layer equations with these conditions give solutions that describe accurately the velocity and temperature fields of very hot planar and round jets and also of very cold plane jets in the far field region where the density and temperature differences are comparable to the ambient values. Simple scaling arguments indicate that the point source description does not apply, however, to cold round jets, whose far field region is not large compared with the jet development region, as verified by numerical integrations.This collaborative research was supported by the Spanish MICINN under Project # ENE2008-06515-C04 and by the Comunidad de Madrid under Project# S2009/ENE-1597 (HYSYCOMB

Confined axisymmetric laminar jets with large expansion ratios

This paper investigates the steady round laminar jet discharging into a coaxial duct when the jet Reynolds number, Re/sub j/, is large and the ratio of the jet radius to the duct radius, epsiv, is small. The analysis considers the distinguished double limit in which the Reynolds number Re/sub a/=Re/sub j/epsiv for the final downstream flow is of order unity, when four different regions can be identified in the flow field. Near the entrance, the outer confinement exerts a negligible influence on the incoming jet, which develops as a slender unconfined jet with constant momentum flux. The jet entrains outer fluid, inducing a slow backflow motion of the surrounding fluid near the backstep. Further downstream, the jet grows to fill the duct, exchanging momentum with the surrounding recirculating flow in a slender region where the Reynolds number is still of the order of Re/sub j/. The streamsurface bounding the toroidal vortex eventually intersects the outer wall, in a non-slender transition zone to the final downstream region of parallel streamlines. In the region of jet development, and also in the main region of recirculating flow, the boundary-layer approximation can be used to describe the flow, while the full Navier-Stokes equations are needed to describe the outer region surrounding the jet and the final transition region, with Re/sub a/=Re/sub j/epsiv entering as the relevant parameter to characterize the resulting non-slender flows

Viscoacoustic squeeze-film force on a rigid disk undergoing small axial oscillations

This paper investigates the air flow induced by a rigid circular disk or piston vibrating harmonically along its axis of symmetry in the immediate vicinity of a parallel surface. Previous attempts to characterize these so-called 'squeeze-film' systems largely relied on simplifications afforded by neglecting either fluid acceleration or viscous forces inside the thin enclosed gas layer. The present viscoacoustic analysis employs the asymptotic limit of small vibration amplitudes to investigate the flow by systematic reduction of the Navier-Stokes equations in two distinct flow regions, namely, the inner gaseous film where streamlines are nearly parallel to the confining walls and the near-edge region of non-slender flow that features gas exchange with the surrounding stagnant atmosphere. The flow in the gaseous film depends on the relevant Stokes number, defined as the ratio of the characteristic viscous time across the film to the characteristic oscillation time, and on a compressibility parameter, defined as the square of the ratio of the acoustic time for radial pressure equilibration to the oscillation time. A Strouhal number based on the local residence time emerges as an additional governing parameter for the near-edge region, which is incompressible at leading order. The method of matched asymptotic expansions is used to describe the solution in both regions, across which the time-averaged pressure exhibits comparable variations that give opposing contributions to the resulting time-averaged force experienced by the disk or piston. A diagram structured with the Stokes number and compressibility parameter as coordinates reveals that this steady squeeze-film force, typically repulsive for small values of the Stokes number, alternates to attraction across a critical separation contour in the parametric domain that exists for all Strouhal numbers. This analysis provides, for the first time, a unifying viscoacoustic theory of axisymmetric squeeze films, which yields a reduced parametric description for the time-averaged repulsion/attraction force that is potentially useful in applications including non-contact fluid bearings and robot locomotion