Slip velocity and lift
Slip velocity and lift
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DOI：
10.1017/s0022112001007145
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发表时间：
2002-03-10
影响因子：
3.7
通讯作者：
Ocando, D
中科院分区：
文献类型：
--
作者：
Joseph, DD;Ocando, D
本文用直接数值模拟方法研究了垂直于重力方向的平面Poillille流中圆形颗粒所受的升力。角滑移速度Ω（s）= Ω（p）+ 1/2（gamma）over dot，其中-1/2（gamma）over dot是在剪切速率为（gamma）over dot的点处流体的角速度，Ω（p）是颗粒的角速度，在流体动力学升力平衡浮力的平衡位置处，角滑移速度Ω（s）总是正的。粒子迁移到其平衡位置并调整Omega（p），使得Omega（s）> 0几乎为零，因为Omega（p）近似于点上的-1/2（gamma）。无论粒子被放置在哪里，它都会以唯一的、稍微正的平衡角滑移速度漂移到平衡位置。角滑移速度差定义为迁移粒子的角滑移速度与其平衡位置处的角滑移速度之间的差，在平衡位置以下为正，在平衡位置以上为负。对于中性浮力粒子，该差是在平衡位置以上和以下改变符号的量，对于重粒子，该差也是在较低平衡位置以上和以下改变符号的量。讨论了新发现的转折点跃迁和中心线附近的不稳定平衡位置的存在性和性质，修正了Choi & Joseph（2001）的长粒子模型，给出了粒子速度和穿过粒子中心线通道的速度分布的显式公式，使之包括粒子旋转的影响。考虑到模型的简单性，UP和速度分布的显式公式与模拟值惊人地吻合。当颗粒不存在时，在颗粒中心点处的Poiffille流动速度的值总是大于颗粒速度;在稳定流动时，滑移速度为正。
The lift force on a circular particle in plane Poiseuille flow perpendicular to gravity is studied by direct numerical simulation. The angular slip velocity Omega(s) = Omega(p) + 1/2(gamma) over dot, where -1/2(gamma) over dot is the angular velocity of the fluid at a point where the shear rate is (gamma) over dot and Omega(p) is the angular velocity of the particle, is always positive at an equilibrium position at which the hydrodynamic lift balances the buoyant weight. The particle migrates to its equilibrium position and adjusts Omega(p) so that Omega(s) > 0 is nearly zero because Omega(p) approximate to -1/2(gamma) over dot. No matter where the particle is placed, it drifts to an equilibrium position with a unique, slightly positive equilibrium angular slip velocity. The angular slip velocity discrepancy defined as the difference between the angular slip velocity of a migrating particle and the angular slip velocity at its equilibrium position is positive below the position of equilibrium and negative above it. This discrepancy is the quantity that changes sign above and below the equilibrium position for neutrally buoyant particles, and also above and below the lower equilibrium position for heavy particles. The existence and properties of unstable positions of equilibrium due to newly identified turning-point transitions and those near the centreline are discussed.The long particle model of Choi & Joseph (2001) that gives rise to an explicit formula for the particle velocity and the velocity profile across the channel through the centreline of the particle is modified to include the effect of the rotation of the particle. In view of the simplicity of the model, the explicit formula for Up and the velocity profile are in surprisingly good agreement with simulation values. The value of the Poiseuille flow velocity at the point at the particle's centre when the particle is absent is always larger than the particle velocity; the slip velocity is positive at steady flow.