喷溅水滴在白噪声激励下的运动特性

Motion characteristics of splashing water droplets under white noise excitation

针对溅抛水滴在水舌风场的随机运动机制的科学问题,基于布朗运动的机制,提出运动于坝下游空间的挑流喷溅水滴,会受到大量气体分子的碰撞而产生随机力的物理思想,建立水滴运动随机微分方程,并应用量纲分析方法,获得了扩散系数的数学表达式,进而确立了水滴随机运动数学模型。应用该模型计算得到了随机力作用下水滴运动速度和运动轨迹的变化规律;并对溅水实验进行了数值模拟,计算得到的喷溅范围更接近于实验观测值,验证了水滴随机运动数学模型的正确性。

Considering the random motion mechanism of splashing water droplets in the wind field around water nappes and the mechanism of Brownian random motion,we work out a physical idea-that splashing water droplets moving in the space downstream of a dam are affected by the collision of a large number of gas molecules and generate random forces.We derive a differential equation for the random motion of water droplets and obtain a mathematical expression of the diffusion coefficient using the dimensional analysis method.Then,a mathematical model for the random motion of water droplets is constructed.It is used to calculate the changes in the velocity and trajectory of water droplets under the random forces;A numerical experiment of water splashing is conducted.The splashing ranges it calculates are close to the experimental observations in previous studies,verifying its rationality and accuracy in simulating the random motion of water droplets.