火旋风周围常密度边界层模型
A model for the constant-density boundary layer surrounding fire whirls
AI总结：
本文研究火旋风周围冷边界层的稳态轴对称结构，结合Taylor自相似解与线涡解描述无粘旋流，通过数值积分和匹配渐近展开分析不同旋流水平下的边界层发展，为火旋风数学建模提供一致边界条件。
摘要：
本文研究了水平表面上局部燃料源上方发展起来的火旋风周围冷边界层流动的稳态轴对称结构。边界层外的无粘旋流运动由燃烧产物热浮力湍流卷吸驱动，其通过无旋解描述，该解结合了轴向平面内运动的Taylor自相似解与环量2πΓ的线涡诱导的方位角运动。从指定径向位置开始的边界层发展通过数值积分确定，针对不同旋流水平（由初始径向位置处的径向与方位角速度比σ值衡量）。如Burggraf等人（Phys. Fluids, 1971）开创性边界层分析中处理的σ=0情形，无粘流动向心加速度产生的压力梯度会形成显著径向内流。特别关注边界层速度在轴线附近的终端形态，其呈现三层结构，通过匹配渐近展开描述。所得复合展开式（通过参数σ依赖环境旋流水平）作为边界条件，用于描述边界层流动在轴线附近偏转形成垂直旋流射流。针对不同σ值，给出了所得非细长碰撞区域的数值解，包括无粘流动和具有中等大控制雷诺数Γ/ν的粘性流动。所提供的速度描述对局部火旋风流动的数学建模有用，提供了考虑环境旋流水平的一致边界条件。
英文摘要：
This paper investigates the steady axisymmetric structure of the cold boundary-layer flow surrounding fire whirls developing over localized fuel sources lying on a horizontal surface. The inviscid swirling motion found outside the boundary layer, driven by the entrainment of the buoyant turbulent plume of hot combustion products that develops above the fire, is described by an irrotational solution, obtained by combining Taylor's self-similar solution for the motion in the axial plane with the azimuthal motion induced by a line vortex of circulation $2 πΓ$. The development of the boundary layer from a prescribed radial location is determined by numerical integration for different swirl levels, measured by the value of the radial-to-azimuthal velocity ratio $σ$ at the initial radial location. As in the case $σ=0$, treated in the seminal boundary-layer analysis of Burggraf et al. (Phys. Fluids, 1971), the pressure gradient associated with the centripetal acceleration of the inviscid flow is seen to generate a pronounced radial inflow. Specific attention is given to the terminal shape of the boundary-layer velocity near the axis, which displays a three-layered structure that is described by matched asymptotic expansions. The resulting composite expansion, dependent on the level of ambient swirl through the parameter $σ$, is employed as boundary condition to describe the deflection of the boundary-layer flow near the axis to form a vertical swirl jet. Numerical solutions of the resulting non-slender collision region for different values of $σ$ are presented both for inviscid flow and for viscous flow with moderately large values of the controlling Reynolds number $Γ/ν$. The velocity description provided is useful in mathematical formulations of localized fire-whirl flows, providing consistent boundary conditions accounting for the ambient swirl level.
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