Physics of Wind Musical Instruments

在诸如竖笛、长笛和小号等管乐器中，声音的产生涉及可压缩流体（空气）的运动。这种运动可能非常复杂，并可能导致涡旋的形成和在强驱动流体中发现的其他现象。这种复杂的流体运动通常在管乐器的吹口或靠近诸如音孔之类的狭窄处发现，在那里实验观察是最困难的。该项目将使用先进的计算方法来研究几种管乐器内部和周围空气的流体动力学。这种流体运动直接负责声音的产生，因此这项研究的结果将有助于更好地理解各种管乐器产生的音乐音调。在可能的情况下，计算结果还将与作为本项目一部分的定制仪器或通过其他小组的实验工作获得的实验结果进行比较。参与该项目的本科生和研究生将从事实验工作，也将从事建模工作。这种建模经验将为他们在高级科学计算领域的职业生涯做好准备，因为用于解决乐器的纳维-斯托克斯函数的方法适用于许多技术兴趣问题。描述管乐器流体动力学的物理定律是众所周知的。这些规律用Navier-Stokes方程表示，这是一组非线性偏微分方程，适用于许多涉及流体流动的情况。由于Navier-Stokes方程的复杂性，将其应用于实际的乐器（和其他复杂的系统）需要一个计算解决方案，这在现有的高性能并行计算机上是可行的。该项目将使用被称为“直接数值模拟”的方法来获得各种管乐器的Navier-Stokes方程的解。这将使用最先进的计算资源和为多核计算机体系结构定制设计的算法来实现。这些计算研究将与实验测量相辅相成，旨在测试模型结果的具体预测，从而对这些仪器产生新的见解。还将研究几种假设的新乐器几何形状，这些工作可能会确定产生当前乐器中未发现的特定音调特性的新几何形状。在这个项目中开发的技术将适用于所有管乐器，因此将对音乐声学和其他领域产生广泛的兴趣。

Sound generation in wind instruments such as the recorder, flute, and trumpet involves the motion of a compressible fluid (air). This motion can be extremely complicated, and can lead to vortex formation and other phenomena found in strongly driven fluids. Such complex fluid motion is generally found in the mouthpiece of a wind instrument or near constrictions such as toneholes, where experimental observations are most difficult. This project will use advanced computational methods to study the fluid dynamics of air inside and around several wind instruments. This fluid motion is directly responsible for sound generation, so the results of this study will lead to a better understanding of the musical tones produced by a variety of wind instruments. The computational results will also be compared, where possible, with experimental results obtained with custom made instruments as part of this project or through the experimental work of other groups. The undergraduate and graduate students who will be involved in this project will engage in experimental work and will also work on the modeling. This modeling experience will prepare them for careers in advanced scientific computing, since the methods used to solve the Navier-Stokes for a musical instrument are applicable to many problems of technological interest.The physical laws that describe the fluid dynamics central to wind instruments are well known. These laws are expressed in the Navier-Stokes equations, a set of nonlinear partial differential equations which are applicable to many situation involving fluid flow . The complexity of the Navier-Stokes equations is such that their application to realistic musical instruments (and other complicated systems) demands a computational solution, which is now feasible with available high performance parallel computers. This project will use the approach known as "direct numerical simulation" to obtain solutions of the Navier-Stokes equations for a variety of wind instruments. This will be achieved using state-of-the-art computational resources and custom designed algorithms for multicore computer architectures. These computational studies will be complemented with experimental measurements designed to test specific predictions of the modeling results, leading to new insights into these instruments. Several hypothetical new instrument geometries will also be studied, work that may identify new geometries that produce specific tonal properties not found in current instruments. The techniques that are developed in this project will be applicable in all wind instruments and will therefore be of broad interest to the field of musical acoustics and beyond.