Physics of Wind Musical Instruments

高性能计算机现在已经足够强大，可以根据流体动力学的基本方程对管乐器进行精确的计算研究。该项目的成果将为几乎所有管乐器的基础建模研究铺平道路。从事这项工作的学生将获得可应用于科学和工程中各种其他问题的计算技能。实际上，对管乐器产生的声音进行建模所涉及的方程和计算问题与研究喷气涡轮机产生的声音、扑翼运动、人类发声和其他重要的空气动力学问题所遇到的方程和计算问题相同，因此，参与该项目的学生将精通解决科学中广泛问题所需的高级计算建模方法，工程.学生还将学习可用于制作本项目中建模的乐器的一般实验技能，以及研究这些新乐器所需的数据采集和光谱分析技术。此外，PI将为参加奥本大学外展项目的K-12教师和学生开发声学和乐器教学模块。管乐器（如直笛、长笛、小号和单簧管）中的声音产生涉及可压缩流体（空气）的运动。这种运动可以是极其复杂的，并且可以导致在强驱动流体中发现的涡流形成和各种非线性现象。本提案中描述的项目将使用先进的计算方法来研究各种管乐器内部和周围的空气流体动力学，包括录音机，长笛，小号和单簧管。这种流体运动直接导致声音的产生，因此这项研究的结果将有助于更好地理解管乐器产生的音调。计算结果还将与使用定制仪器进行的实验进行比较，以测试和验证计算结果。管乐器的流体动力学的第一原理描述需要Navier-Stokes方程的解，这是一组非线性偏微分方程。该项目将使用最先进的计算资源和针对多核计算机架构定制设计的算法，获得各种管乐器的Navier-Stokes方程的解。这些计算研究将与旨在测试建模结果的特定定性和定量预测的实验测量相补充，从而对这些仪器产生新的见解。几个假设的新仪器的几何形状将进行研究，工作可能会发现新的设计，产生特定的音调属性没有发现在当前的文书。该项目还将探索如何对玩家的关键方面进行建模，例如玩家嘴唇的运动和通过玩家嘴巴的气流。该项目开发的技术将适用于所有管乐器，因此将在音乐声学领域引起广泛的兴趣。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

High performance computers are now powerful enough to enable accurate computational studies of wind musical instruments based on the fundamental equations of fluid dynamics. The results of this project will pave the way to fundamental modeling studies of virtually all wind instruments. The students who engage in this work will acquire computational skills that can be applied to a variety of other problems in science and engineering. Indeed, modeling the sound produced by a wind instrument involves the same equations and the same computational issues that are encountered in studies of the sound produced by a jet turbine, the motion of a flapping wing, human phonation, and other important aerodynamics problems, so students involved in this project will be well versed in the advanced computational modeling methods needed to tackle a wide range of problems in science and engineering. Students will also learn about general experimental skills that can be used to make the musical instruments modeled in this project, as well as techniques for data acquisition and spectral analysis required in the study of these new instruments. In addition, the PI will develop instructional modules on acoustics and musical instruments for K-12 teachers and students who participate in outreach programs at Auburn University. Sound generation in wind instruments such as the recorder, flute, trumpet, and clarinet involves the motion of a compressible fluid (air). This motion can be extremely complicated, and can lead to vortex formation and various nonlinear phenomena found in strongly driven fluids. The project described in this proposal will use advanced computational methods to study the fluid dynamics of air inside and around a variety of wind instruments, including recorders, flutes, trumpets, and clarinets. 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 wind instruments. The computational results will also be compared with experiments performed with custom made instruments, so as to test and validate the computational findings. A first principles description of the fluid dynamics of a wind instrument requires the solution of the Navier-Stokes equations, a set of nonlinear partial differential equations. This project will obtain solutions of the Navier-Stokes equations for a variety of wind instruments 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 qualitative and quantitative predictions of the modeling results, leading to new insights into these instruments. Several hypothetical new instrument geometries will be studied, work that may identify new designs that produce specific tonal properties not found in current instruments. This project will also explore how to model key aspects of the player, such as the motion of the player’s lips and air flow through the player’s mouth. The techniques that are developed in this project will be applicable to all wind instruments and will therefore be of broad interest in the field of musical acoustics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.