关于气泡坍塌数学模型的一个微分方程
On a differential equation for a gas bubbles collapse mathematical model
AI总结：
本文提出一个数学模型来估计油泵叶片中气泡的坍塌时间，通过将Navier-Stokes方程简化为一个非线性常微分方程，并验证了数值解与线性化解的一致性。
摘要：
本文提出了一个数学模型，用于估计油齿轮泵叶片中气泡的坍塌时间。该时间不能大于泵在单次旋转中填充和排空叶片所花费的总时间，否则内外齿轮之间会失去润滑。我们假设油是不可压缩且具有粘性的，气泡呈球形且不向外部流体平移。模型的解析处理表明，油的Navier-Stokes速度场方程可以简化为一个关于气泡半径随时间变化的非线性常微分方程。通过该方程的数值解估计的坍塌时间与通过线性化方程的解析解计算的坍塌时间基本相等。
英文摘要：
In this paper we present a mathematical model for estimate the collapse time of a gas bubble in a vane of a oil gerotor pump. This amount of time cannot be greater of the total time spent by the pump for filling and then emptying out a vane in a single revolution, otherwise there is a loss of lubrication between internal and external gears. We assume that oil is incompressible and viscous, the bubble has a spherical shape and it is not translating into the external fluid. The analytical treatment of the model shows that the Navier-Stokes equations for the velocity field of the oil can be reduced to a single non linear ordinary differential equation for the variation in time of the bubble radius. The collapse time estimated by a numerical resolution of this equation and the collapse time calculated from an analytical resolution of the linearized equation are substantially equal.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
