Long-time behaviour of the drag on a body in impulsive motion
Long-time behaviour of the drag on a body in impulsive motion
复制标题
冲动运动中物体上的阻力的长期行为
DOI：
10.1017/s0022112095002333
复制
发表时间：
1995
影响因子：
3.7
通讯作者：
R. Mei
中科院分区：
文献类型：
--
作者：
C. Lawrence;R. Mei
我们考虑直线运动的物体上的水动力阻力对两个稳态之间的速度变化的响应，从U1到U2 [ges] 0。我们考虑物体不产生升力的情况，例如对称轴与运动对齐的物体。在大多数情况下，层流尾流由两个准稳定区域——新尾流和旧尾流组成，由一个过渡区连接，过渡区以平均速度U2向下游对流。全球质量平衡表明存在以过渡区为中心的汇流，这是导致非定常力长时间的先导性行为的原因。对于U1 [ges] 0的情况，对于任何有限雷诺数（Re），力都显示出随时间平方反比的代数衰减，并且对于非直线运动也显示出这一结果。最近对包括0 （Re）项在内的小雷诺数的分析（Lovalenti & Brady 1993 A）表明，对于从静止开始的运动，力随着时间的反比平方而衰减，但是对于两个正速度之间的变化，力呈指数衰减。前发现结果是正确的,但是指数衰减O(重新)在后一种情况下是取代在大时间的平方反比衰减时间这是转移到O (Re2公司)因为后通量几乎是常数小再保险。回流的情况下(U1 < 0)和停止流(U2 = 0)分别对待,并表明瞬态力是由旧后的影响,导致较慢的衰变时间的简单的逆。力是由流场的远端区域决定的，因此结果适用于任何（对称）粒子、气泡或水滴，并且（在平均意义上）适用于任何Re，只要τ ma {Re， Re−1}，其中时间τ在对流时间标度中是无因次的。将分析结果与球面颗粒和气泡瞬态流动的详细数值计算结果进行了比较，得到了令人信服的一致性。这些计算被认为是第一次充分解决长时间钝体后瞬态远尾流的计算。应用力的渐近结果来确定自由落体的最终速度也是时间的平方反比。
We consider the response of the hydrodynamic drag on a body in rectilinear motion to a change in the speed between two steady states, from U1 to U2 [ges ] 0. We consider situations where the body generates no lift, such as occur for bodies with an axis of symmetry aligned with the motion. At large times, the laminar wake consists of two quasi-steady regions – the new wake and the old wake – connected by a transition zone that is convected downstream with the mean speed U2. A global mass balance indicates the existence of a sink flow centred on the transition zone, and this is responsible for the leading-order behaviour of the unsteady force at long times. For the case of U1 [ges ] 0, the force is shown to decay algebraically with the inverse square of time for any finite Reynolds number (Re), and this result is also shown to hold for non-rectilinear motions. A recent analysis for small Reynolds number including terms to O(Re) (Lovalenti & Brady 1993 a) has indicated that the force decays as the inverse square of time for motion started from rest, but decays exponentially for a change between two positive velocities. The former result is found to be correct, but the exponential decay at O(Re) in the latter case is superseded at large times by the inverse-square time decay which is shifted to O(Re2) because the wake flux is nearly constant for small Re. The cases of reversed flow (U1 < 0) and stopped flow (U2 = 0) are treated separately, and it is shown that the transient force is dominated by the effects of the old wake, leading to a slower decay as the simple inverse of time. The force is determined by the far regions of the flow field and so the results are valid for any (symmetric) particle, bubble or drop and (in an average sense) for any Re, provided τ ma {Re, Re−1}, where the time τ is made dimensionless with the convection timescale. The analytical results are compared to detailed numerical calculations for transient flow over spherical particles and bubbles and compelling agreement is observed. These are believed to be the first calculations which adequately resolve the transient far wake behind a bluff body at long times. The asymptotic result for the force is applied to determine that the approach to terminal velocity of a body in free fall is also as the inverse square of time.