论文标题
多重湍流中预混合火焰的分形尺寸
Fractal dimension of premixed flames in multifractal turbulence
论文作者
论文摘要
在动荡的预防火焰中，damköhler的大规模限制$（da >> 1）$和$ \ mathbb {d} = 8/3 $ forMathler的小型限制$（MATH）$ nata $ n da $ n da da d da da da da da da d da da d da da da plame iso-sulface的分形尺寸为$ \ mathbb {d} = 7/3 $，对于Damköhler的大规模限制$（DA >> 1）$和$ \ MATHBB {d} = 8/3 $ forMathler的小型级别的$ n o \ sims $ na启发式缩放论点。但是，这种缩放参数并未考虑湍流动能耗散在火焰表面上的多效性质的影响。在本文中，我们说明了多型耗散对低$ da $ turmulentprexprex的火焰的分形尺寸的影响。我们将两次更正到分形维的上限 - $ \ MATHBB {d} = 8/3+3/4（1-D_ {1/4}）$和$ \ Mathbb {d} = 8/3+2/3（3+2/3（3-D_ {1/3}）$ - 到达标准范围内的变化和距离范围的变化。分别是由湍流耗散的间歇性产生的。我们进一步表明，第二个校正会导致分形维度$（\ mathbb {d}）$在速度结构函数的缩放指数$（ξ）$上的明确依赖性：$ \ mathbb {d} = 11/3+ξ$。因此，我们明确量化了湍流对低$ da $预燃烧的多重性质的影响。
In turbulent premixed flames, the fractal dimension of flame iso-surface is argued to be $\mathbb{D}=7/3$ for Damköhler's large-scale limit $(Da>>1)$ and $\mathbb{D}=8/3$ for Damköhler's small-scale limit $(Da\sim\mathcal{O}(1))$ based on heuristic scaling arguments. However, such scaling arguments do not consider the effect of the multifractal nature of turbulent kinetic energy dissipation on the flame surface. In this paper, we account for the effects of multifractal dissipation on the fractal dimension of low $Da$ turbulent premixed flames. We derive two corrections to the upper-limit of fractal dimension -- $\mathbb{D}=8/3+3/4(1-D_{1/4})$ and $\mathbb{D}=8/3+2/3(3-D_{1/3})$ -- which correspond to the change in the scalar flux and the total area of flame interface due to fluctuations in the inner cut-off scale arising from the intermittent nature of turbulent dissipation, respectively. We further show that the second correction leads to an explicit dependence of the fractal dimension $(\mathbb{D})$ on the scaling exponent $(ξ)$ of the velocity structure function through the relation: $\mathbb{D}=11/3+ξ$. Thus, we explicitly quantify the effect of the multifractal nature of turbulence upon low $Da$ premixed combustion.
