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arXiv 2302.05074physics.flu-dyn
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低马赫数模型中层流火焰速度与温度微分方程的耦合公式

Formula of Laminar Flame Speed Coupled with Differential Equation for Temperature in Low-Mach-Number Model

Keigo Wada

摘要:

温度的非单调分布应考虑管内燃烧或热核火焰的情况,这可能会加速成为爆震波。这种转变被称为燃烧转爆轰。针对这一点,我们扩展了绝热火焰的研究,假设零温度梯度在燃烧侧边缘的火焰前锋,非零温度梯度的情况下,通过引入压缩区后面的前面。这样的处理已经在以前的工作中进行的基础上的点火温度近似。在这种情况下,气体压缩对火焰的影响是由关于小平方马赫数的渐近解来描述的:例如,在压缩区,内部解用Lambert $W$函数来表示。然而,由于目的是获得解析解内的火焰前锋,反应项的温度依赖性被忽略,因此,冷边界困难没有得到认真对待。这个问题是解决在这项研究中使用的大活化能渐近的反应项所表示的Arrhenius类型。反应区的温度分布采用数值计算,压缩区的温度分布采用解析计算。本文还考虑了燃烧速率特征值问题,导出了层流火焰速度公式,并与反应区温度微分方程耦合。然后,层流火焰速度对热扩散参数的依赖性,伴随着由压缩效应带来的流体动力学特性,变得清晰。在非零马赫数马赫数条件下,得到了火焰阵面燃烧侧温度梯度非零的条件。

英文摘要:

The non-monotonic profile of temperature is to be considered in the context of combustion inside tubes or thermonuclear flames, which may accelerates to become detonation waves. This transition is known as deflagration-to-detonation transition. Focusing on this point, we extend the study of adiabatic flames, which assumes zero temperature gradient at the burned-side edge of a flame front, to the case of non-zero temperature gradient by introducing compression zone behind the front. Such a treatment has been performed in the previous work based on the ignition temperature approximation. In that case, the effect of gas compression on flames was described by asymptotic solutions with respect to small squared Mach numbers: for example, in the compression zone, inner solutions are expressed by use of Lambert $W$ function. However, due to the aim of obtaining analytical solutions inside a flame front, the temperature dependence of reaction term was ignored and, as a result, the cold boundary difficulty was not treated seriously. This issue is resolved in this study by use of large activation energy asymptotics with the reaction term expressed by the Arrhenius type. The temperature distribution is computed numerically in the reaction zone and calculated analytically in the compression zone. The burning-rate eigenvalue problem is also considered to derive a formula of laminar flame speed, which is coupled with differential equation for temperature in the reaction zone. Then, the dependence of laminar flame speed on thermal-diffusive parameters, accompanied with hydrodynamic properties brought by the compression effect, becomes clear. The non-zero gradient condition of temperature on the burned side of a flame front is obtained for non-zero values of Mach number.

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