School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran.
Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, Indiana 46556, USA.
Phys Rev E. 2017 May;95(5-1):053301. doi: 10.1103/PhysRevE.95.053301. Epub 2017 May 1.
The available lattice Boltzmann (LB) models for combustion or phase change are focused on either single-phase flow combustion or two-phase flow with evaporation assuming a constant density for both liquid and gas phases. To pave the way towards simulation of spray combustion, we propose a two-phase LB method for modeling combustion of liquid fuel droplets. We develop an LB scheme to model phase change and combustion by taking into account the density variation in the gas phase and accounting for the chemical reaction based on the Cahn-Hilliard free-energy approach. Evaporation of liquid fuel is modeled by adding a source term, which is due to the divergence of the velocity field being nontrivial, in the continuity equation. The low-Mach-number approximation in the governing Navier-Stokes and energy equations is used to incorporate source terms due to heat release from chemical reactions, density variation, and nonluminous radiative heat loss. Additionally, the conservation equation for chemical species is formulated by including a source term due to chemical reaction. To validate the model, we consider the combustion of n-heptane and n-butanol droplets in stagnant air using overall single-step reactions. The diameter history and flame standoff ratio obtained from the proposed LB method are found to be in good agreement with available numerical and experimental data. The present LB scheme is believed to be a promising approach for modeling spray combustion.
现有的格子玻尔兹曼（LB）燃烧或相变模型主要集中在单相流燃烧或具有蒸发的两相流上，假设液相和气相的密度保持不变。为了为喷雾燃烧模拟铺平道路，我们提出了一种用于模拟液体燃料液滴燃烧的两相 LB 方法。我们开发了一种 LB 方案，通过考虑气相中的密度变化并基于 Cahn-Hilliard 自由能方法考虑化学反应来模拟相变和燃烧。通过在连续性方程中添加由于速度场的散度不为零而导致的源项来模拟液体燃料的蒸发。在控制纳维-斯托克斯方程和能量方程中使用低马赫数近似来包含由于化学反应、密度变化和非发光辐射热损失引起的源项。此外，通过包含由于化学反应引起的源项来制定化学物质的守恒方程。为了验证模型，我们考虑了在静止空气中的正庚烷和正丁醇液滴的燃烧，使用整体单步反应。发现所提出的 LB 方法得到的直径历史和火焰脱离比与现有数值和实验数据吻合良好。本 LB 方案被认为是一种有前途的喷雾燃烧模拟方法。
