научная статья по теме LARGE EDDY SIMULATION OF HYDROGEN-AIR EXPLOSION AT ELEVATED TEMPERATURE Химия

Текст научной статьи на тему «LARGE EDDY SIMULATION OF HYDROGEN-AIR EXPLOSION AT ELEVATED TEMPERATURE»

ХИМИЧЕСКАЯ ФИЗИКА, 2004, том 23, № 8, с. 25-36

ХИМИЯ АТМОСФЕРЫ

УДК 536.46:614.83

LARGE EDDY SIMULATION OF HYDROGEN-AIR EXPLOSION AT ELEVATED TEMPERATURE

© 2004 V. V. Molkov*, D. V. Makarov

University of Ulster, Newtownabbey, Co. Antrim, Northern Ireland,, BT37 0QB, UK

Received 01.10.2003

The LES model of flame propagation and pressure build up during gaseous explosions in large-scale closed vessels is suggested. The subgrid scale turbulence modelling is based on the renormalization group approach. The premixed combustion is modelled by the gradient method and based on the filtered progress variable equation. The full three-dimensional compressible Navier-Stokes equations are solved on unstructured tetrahedral meshes in a spherical domain of 2.3-m diameter. The average size of the tetrahedron edges was 0.07 cm for uniform grid and 0.035 m with one level of solution adaptive grid refinement/derifinement around the flame front area. The simulations were validated against experimental data by Kumar et al. on deflagration of a stoichiometric hydrogen-air mixture, initiated at the centre of a closed sphere of 2.3-m diameter at initial temperature 100°C and pressure 97 kPa. The simulated pressure dynamics is in agreement with the experiment. The role of a mesh size on the resolved flame wrinkling factor and pressure build up is demonstrated in the assumption of subgrid scale wrinkling ssgs = 1. For the first time the resolved cellular structure (wrinkling) of a large-scale explosion flame is obtained by LES. The resolved flame front wrinkling factor increases with flame radius and reaches S = 1.09 on the 0.035 m mesh.

INTRODUCTION

More than 2 000 explosions occur in Europe annually [1]. Nearly 1 000 combined fire and explosion accidents occur in the UK alone every year [2]. Explosion safety engineering requires contemporary validated tools for risk assessment and safe design of structures [3]. The fire-related deflagrations such as a backdraught are the problem too [4]. The improvement of models, verification and validation of numerical simulations against experimental data will be of great importance in the foreseeable future [5, 6].

Computational fluid dynamics (CFD) modeling has been developing for years to predict consequences of explosions. Mainly the Reynolds averaged Navier-Stokes (RANS) approach has been employed to simulate accidental gaseous deflagrations. The general theoretical framework of RANS for explosion simulation is published elsewhere, e.g. [7] and is implemented in such codes as EXSIM, FLACS, AutoReagas, etc. There is a criticism of applying combustion models, in particular the eddy break-up model, as they require ad hoc corrections to obtain realistic flame shapes and often are predicting an order of magnitude error in the overpressures [3]. A laminar flamelet model with algebraic expression for the flame surface area has been used on an unstructured solution adaptive numerical grid system in the framework of the RANS approach by Cant et al. [3]. Authors estimated the overall accuracy as inadequate and concluded that the need for improved mod-

Corresponding author. Tel.: +44(0)2890-368731; fax: +44(0)2890-368700. E-mail: v.molkov@ulster.ac.uk

elling is clear, particularly in the initial laminar phase of flame development [3].

Large eddy simulation (LES) is regarded as an improvement on existing CFD techniques as it holds advantages over traditional RANS approaches [8]. In particular, interactions between turbulence and flame structure at scales comparable with filter width could be resolved in space and time. The filter width for the most common choice in practice is represented numerically by grid spacing to minimize computational costs and one has to accept the consequence that the " marginal" eddies may not be well resolved. However, if one expects to adequately resolve large scales down to filter width it is natural to require that a filter size be several times larger than mesh size [9]. The LES modelling of turbulent combustion encounters difficulties not present in modelling momentum transport, in which the main effect of unresolved small scales is to provide dissipation [10]. The difficulty is more pronounced in premixed (explosions) in comparison with non-premixed (fires) combustion, where infinite rate chemistry can be assumed to a first approximation to eliminate effects of the small scales.

Problems encountered in LES of accidental explosions are quite different from those in LES of turbulent premixed combustion in engines, etc. Two main features making this difference are problem scales, which are larger in orders of magnitude for explosions with corresponding decrease of flame stretch rate effects, and initial conditions, i.e. explosions often commence in quasi-quiescent mixture. The present study seems the first devoted to LES of large-scale explosions.

Direct simulation of large flow structures by LES opens the way to resolve flame front wrinkling to some extent depending on mesh size. Indeed, the observations during SOLVEX experiments performed in a 547 m3 vessel revealed that the characteristic cell sizes of methane-air and propane-air explosion flames are large enough and increasing from about 15 cm to 40 cm with flame front radius growth from about 1 to 3 m [11]. According to Groff [12], for stoichiometric propane-air deflagration the onset of cellular structure due to hydro-dynamic instability occurs at the flame Reynolds number about 104 when the flame radius is 0.056 m. If this critical value is accepted for hydrogen-air flame (|u = = 2.3 ■ 10-5 Pa ■ s, pu = 0.66 kg ■ m-3) then one can estimate that the flame could become hydrodynamically unstable at the flame radius Rff = (Re iJASUpJ = 0.08 m.

In most of approaches to LES of premixed combustion there is a numerical requirement for a minimum number of computational grid points within the simulated flame front thickness, normally 4-5 points [8]. For hexahedral grids it means that a flame front occupies 4-5 cells. In LES a local simulated flame thickness is expected to be of approximately the same order as a filter size and, at the same time, it should be adequately resolved on the computational grid to avoid numerical difficulties associated with insufficient resolution [8]. Not less than four computational cells were required for the resolution of the premixed turbulent flame in 2D RANS simulations [18]. The numerical flame width of 3-7 grid intervals was used for 2D RANS simulations of premixed turbulent combustion in [22]. This numerical flame width also provides a cut-off length scale below which the developing of structures is suppressed, but longer wavelength instabilities are successfully resolved [22]. However, for tetrahedral unstructured grids 4-5 points through the flame front can be "collected" at the distance equal to 2-3 edges of tetrahedral. So, experimentally observed flame front cells of hydro-dynamic nature could be resolved by LES when their size is larger than about 4-6 edges of tetrahedron of the mesh.

For hydrogen-air flames at normal temperature and pressure stable preferential-diffusion conditions (positive Markstein number, Ma) are observed at fuel-equivalence ratios above roughly 0.7 [13]. The neutral preferential-diffusion condition (Ma = 0) shifts toward fuel-rich conditions with increasing pressure [14]. It could lead to the development of preferential-diffusion instability at pressures above 4 atm when one could expect that chaotically irregular surfaces will develop. Experimental data on influence of temperature on hydrogen-air flame instabilities are not available. However, a stabilizing effect of temperature growth could be assumed as the burning velocity is increasing with temperature. That could compensate for the destabilizing influence of growing pressure.

Preferential-diffusion affects the flame front structure at scales comparable with real flame front thick-

ness due to its molecular transport nature. The strongest effect of preferential diffusion coupled with flame stretch and curvature effects is at radii below 1 cm for various fuel-equivalence ratios. Instabilities still were observed for hydrogen-air flames with stable preferential-diffusion, including stoichiometric hydrogen-air mixture at normal conditions [13]. However, irregular cellular-like instabilities only appeared when flame radii were relatively large, and "probably were caused by hydrodynamic instabilities, similar to the earlier observations of Groff [12]" for propane-air mixtures [13]. It is important to stress that the mechanism of preferential-diffusion is not effective on the scales of the cells observed for hydrodynamic instability [15]. Only hy-drodynamic instability could be resolved by LES at scales of explosions and effects of preferential-diffusion (if any) should be taken into account by value of burning velocity.

The concept of burning velocity, Su, provides a convenient way to take into account the influence of changing pressure and temperature on explosion dynamics during simulations. The fuel consumption rate may be estimated from the unburned gas density and the burning velocity as PuSu.

Often, accidental deflagration commences in a quiescent mixture and the following regimes of flame propagation can be identified: 1) stable laminar flame propagation, 2) unsteady flame cracking and cell formation, 3) cellular flame propagation, 4) self-turbuliz-ing flame propagation [16]. The purely laminar regime, unsteady flame cracking and cell formation regime are of practically no interest for explosion safety engineering as they can only exist at scales not more than some centimeters. According to available experimental data cellular flame propagation takes place up to at least some meters. Answers on questions "what" is the nature of transition from cellular to self-turbulizing flame and "when" it happens are not clear. Many authors suggest that though the highest overpressures are generat

Для дальнейшего прочтения статьи необходимо приобрести полный текст. Статьи высылаются в формате PDF на указанную при оплате почту. Время доставки составляет менее 10 минут. Стоимость одной статьи — 150 рублей.

Показать целиком