摘要:

The canonical problem of the one-dimensional, pulsating, overdriven detonation wave has been studied for over 30 years, not only for its phenomenological relation to the evolution of multidimensional detonation instabilities, but also to provide a robust, reactive, high-speed flowfield with which to test numerical schemes. The present study examines this flowfield using high-order, essentially non-oscillatory schemes, systematically varying the level of resolution of the reaction zone, the size and retention of information in the computational domain, the initial conditions, and the order of the scheme. It is found that there can be profound differences in peak pressures as well as in the period of oscillation, not only for cases in which the reaction front is under-resolved, but for cases in which the computation is corrupted due to a too-small computational domain. Methods for estimating the required size of the computational domain to reduce costs while avoiding erroneous solutions are proposed and tested.

ISSN:1364-7830    

DOI:10.1088/1364-7830/4/3/301

出版商:Taylor & Francis    

年代:2000

数据来源: Taylor

摘要:

A recently developed spectral model for premixed turbulent combustion in the flamelet regime (based on the EDQNM turbulence theory) has been compared with both direct numerical simulations (DNS) and experimental data. The 1283DNS is performed at a Reynolds number of 223 based on the integral length scale. Good agreement is observed for both single- and two-point quantities (i.e. ratio of the turbulent to laminar burning velocities, scalar autocorrelation, dissipation and scalar-velocity cross correlation spectra) for the two different values ofu′/sL0considered. The model also predicts the rapid transient behaviour of the flame at early times. An experimental set-up is then described for generating a lean methane-air flame and measuring two-point spatial correlations along the midpoint of the flame brush (i.e. along the C¯=0.5 contour). The experimental measurements in the flamelet regime take the form of a discontinuous or ‘telegraph’ signal. The EDQNM model, in contrast, describes an ‘ensemble’ of flames, and thus is based solely on continuous variables. A theoretical relationship between the correlation obtained from the EDQNM model and the equivalent correlation for a discontinuous (experimental) flame is derived. The relationship is used to enable a meaningful comparison between experimentally observed and model correlations. In general, the agreement is good for the three different cases considered in this study, with most of the error occurring at the lowest Reynolds number (ReL=22). Furthermore, it is shown that considerably more error would result if no attempt is made to convert the ensemble representation in the model to an equivalent single-flame or ‘telegraph’ signal.

ISSN:1364-7830    

DOI:10.1088/1364-7830/4/3/302

出版商:Taylor & Francis    

年代:2000

数据来源: Taylor

摘要:

The time-dependent evolution of the radical pool in an initially inert hydrogen-air counterflow mixing layer subject to variable strain is investigated analytically. Although the initial chemistry description contains three different chain carriers, namely, H, O and OH, it is shown that the ignition problem can be accurately described in terms of a single radical-pool variable that incorporates steady-state assumptions for the radicals O and OH. Use of this non-standard procedure reduces the problem to the integration of a single conservation equation, whose solution depends on the existing Damköhler number Δ, defined as the ratio of the diffusion time across the mixing layer to the characteristic branching time. Ignition takes place when Δ remains predominantly above a critical value of the order of unity. The exponentially growing radical pool, which extends across the mixing layer, can be described analytically by separation of variables in configurations with a slowly varying strain rate, providing a solution that is used to investigate the parametric dependences of the ignition time. Weakly strained solutions are studied separately by addressing the asymptotic limit of large Damköhler numbers. It is seen that the reaction zone then becomes a thin layer of relative thickness Δ−1/4centred at the location where the branching rate is maximum. The analysis employs asymptotic expansions in decreasing powers of Δ for the shape and for the exponential growth rate of the radical pool. The accurate description of the solution necessitates computation of three terms in the asymptotic expansion for the growth rate, yielding predictions for the ignition time that remain accurate even for values of Δ of the order of unity.

ISSN:1364-7830    

DOI:10.1088/1364-7830/4/3/303

出版商:Taylor & Francis    

年代:2000

数据来源: Taylor

摘要:

The effect of the presence of a spray of liquid fuel on thermal explosion in a combustible droplet-gas cloud is investigated. By ‘thermal explosion’ we refer exclusively to the initial stages of the behaviour of the combustible medium as its temperature begins to rise and various competing physical and chemical processes are called into play. A qualitative analysis of the system of governing equations is carried out using an advanced geometrical asymptotic technique (the integral manifold method). Possible types of dynamical behaviour of the system are classified and parametric regions of their existence are determined analytically. It is demonstrated that the original problem can be decomposed into two subproblems, due to the underlying hierarchical time scale structure. The first subproblem relates to the droplet heat up period, for which a relatively rapid time scale is applicable. The second subproblem begins at the saturation point. For the latter, more significant second stage, it is found that there are five main dynamical regimes: slow regimes, conventional fast explosive regimes, thermal explosion with freeze delay and two different types of thermal explosion with delay (the concentration of the combustible gas decreases or increases). Upper and lower bounds for the delay time are derived analytically and compared with results of numerical simulations, with rather satisfactory agreement.

ISSN:1364-7830    

DOI:10.1088/1364-7830/4/3/304

出版商:Taylor & Francis    

年代:2000

数据来源: Taylor

摘要:

Borrowing the structure of building blocks from potential hydrodynamics, we set up model evolution equations to mimic moderately wrinkled three-dimensional flames expanding in gaseous premixtures. These evolution equations incorporate a hydrodynamic instability, local curvature effects, a Huygens-type nonlinearity, and can cope with broad-banded forcing whenever needed. Pseudo-spectral integrations in the Legendre–Fourier basis yield evolutions of the whole front that are in striking qualitative agreement with experiments on free or weakly forced propagations. Our results are robust against educated changes in the modelling. Provided an accurate evolution equation is available, this approach can simulate expanding flames which are quite a bit larger than what DNS can currently handle, at least in the chosen configurations.

ISSN:1364-7830    

DOI:10.1088/1364-7830/4/3/305

出版商:Taylor & Francis    

年代:2000

数据来源: Taylor

摘要:

We present a simple and general reduction algorithm for stiff monomolecular kinetic systems. The reduction is based on algebraic techniques and consists in eliminating the fastest dynamics in the initial system without any change of basis. This process is systematic and is not based on chemical conventional assumptions or on singular perturbation techniques. Systems can be reduced even if they are not in the Tikhonov form. This reduction process is applied to kinetic systems with kinetic constants belonging to different scales. Error estimates for all species are given. Numerical tests are performed.§Part of this work was carried out during the 1997-1998 year at the Department of Mathematics at MIT, USA.

ISSN:1364-7830    

DOI:10.1088/1364-7830/4/3/306

出版商:Taylor & Francis    

年代:2000

数据来源: Taylor