An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion
An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion
复制标题
验证非预混湍流燃烧中火焰近似的基本模型
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
A. Majda
中科院分区：
文献类型：
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作者：
A. Bourlioux;A. Majda
在一个理想模型问题的基础上，结合了非预混火焰的层流渐近理论和被动标量扩散的严格均匀化理论的思想，检验了三种非预混湍流燃烧的小火焰模型的基本可靠性。总体火焰构型由被动标量中的平均梯度来稳定：层流情况的大Damköhler数渐近结果可用于量化导致火焰偏离其平衡状态的有限速率效应；同样的结果也可用于将高阶修正纳入以被动标量表示的被动变量的近似中。这种火焰小波近似的使用已经远远超出了层流状态，因为它们是模拟湍流状态下非预混火焰的实用策略的核心：火焰小波表示通过用可能更简单的被动标量闭合问题取代反应变量的湍流闭合问题，从而避免了反应变量的湍流闭合问题。本文在一类小尺度周期流的理想化背景下讨论的，正是层流状态之外的这种替代的有效性，对于此类小尺度周期流，被动标量统计可以得到广泛的严格结果。这里报告了这个简化问题的结果，其中有很大范围的Peclet和Damköhler数字。在Damköhler数方面观察到渐近收敛，其收敛率与层流预测相匹配，并且对Peclet数相对不敏感。被动标量耗散在有限速率情况下实现高阶修正中起着关键作用：用平均值代替其逐点值在实际中是方便的，并且对于本文研究的流动类别可以严格激励，但是，虽然它确实实现了对低阶平衡模型的总体改进，但简化妥协了与原始有限速率火焰模型观察到的具有精确局部耗散的较高渐近收敛性。（本文中部分数字仅为电子版，详见www.iop.org）
The fundamental soundness of three flamelet models for non-premixed turbulent combustion is examined on the basis of their performance in an idealized model problem that merges ideas from the laminar asymptotic theory for non-premixed flames and rigorous homogenization theory for the diffusion of a passive scalar. The overall flame configuration is stabilized by a mean gradient in the passive scalar: large Damköhler number asymptotics results are available for the laminar case to quantify the finite-rate effects that cause the flame to depart from its equilibrium state; the same results can also be used to incorporate higher-order corrections in the approximation of the reactive variables in terms of the passive scalar. The use of such flamelet approximations has been extended well beyond the laminar regime as they lie at the core of practical strategies to simulate non-premixed flames in the turbulent regime: the flamelet representation avoids the problem of turbulence closure for the reactive variables by replacing it by the presumably much simpler closure problem for a passive scalar. It is precisely the validity of this substitution outside the laminar regime that is addressed here in the idealized context of a class of small-scale periodic flows for which extensive rigorous results are available for the passive scalar statistics. Results for this simplified problem are reported here for significant wide ranges of Peclet and Damköhler numbers. Asymptotic convergence is observed in terms of the Damköhler number, with a convergence rate that is found to match the laminar predictions and appears relatively insensitive to the Peclet number. The passive scalar dissipation plays a key role in achieving higher-order corrections for the finite-rate case: replacing its pointwise value by an averaged value is convenient practically and can be rigorously motivated for the class of flows studied here, but while it does achieve an overall improvement over the lower-order equilibrium model, the simplification compromises the higher asymptotic convergence observed with the original finite-rate flamelet model with exact local dissipation.(Some figures in this article are in colour only in the electronic version; see www.iop.org)