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A Swing of Beauty: Pendulums, Fluids, Forces, and Computers

机译:美容的摇摆:摆锤,液体,力量和计算机

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摘要

While pendulums have been around for millennia and have even managed to swing their way into undergraduate curricula, they still offer a breadth of complex dynamics to which some has still yet to have been untapped. To probe into the dynamics, we developed a computational fluid dynamics (CFD) model of a pendulum using the open-source fluid-structure interaction (FSI) software, IB2d. Beyond analyzing the angular displacements, speeds, and forces attained from the FSI model alone, we compared its dynamics to the canonical damped pendulum ordinary differential equation (ODE) model that is familiar to students. We only observed qualitative agreement after a few oscillation cycles, suggesting that there is enhanced fluid drag during our setup’s initial swing, not captured by the ODE’s linearly-proportional-velocity damping term, which arises from the Stokes Drag Law. Moreover, we were also able to investigate what otherwise could not have been explored using the ODE model, that is, the fluid’s response to a swinging pendulum—the system’s underlying fluid dynamics.
机译:虽然摆锤是千年的,但甚至甚至设法进入本科课程,他们仍然提供了一系列复杂的动态,其中一些尚未尚未开发。为了探测到动态,我们使用开源流体结构交互(FSI)软件IB2D开发了一个柱形的计算流体动力学(CFD)模型。除了单独的FSI模型中实现的角位移,速度和力之外,我们将其动力学与学生熟悉的规范阻尼摆动普通微分方程(ODE)模型进行了比较。我们只观察到几个振荡周期后的定性协议,这表明在我们的设置初始摆动期间有增强的流体阻力,而不是由颂歌的线性比例速度阻尼项捕获,这是由Stokes拖拉法产生的。此外,我们还能够使用ode模型来研究否则无法探索的,即流体对摆动摆的响应 - 系统的底层流体动力学。

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