Physics of Wind Musical Instruments

在诸如录音机、长笛、小号和单簧管等管乐器中，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各种非线性现象。佐丹诺博士将使用先进的计算方法来研究各种风力设备内部和周围的空气流体动力学。这种流体运动直接导致了声音的产生，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乐音调。该项目的一个组成部分将是将计算结果与使用真实仪器进行的实验进行比较，以检验和验证计算结果。从事这项工作的学生将获得计算技能，这些技能可以应用于科学和工程中的各种其他问题。事实上，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、拍打机翼的运动、人体发声和其他重要的空气动力学问题时遇到的方程和计算问题相同，因此参与本项目的学生将非常精通解决科学和工程中的广泛问题所需的高级计算建模和实验方法。风仪器流体动力学的第一性原理描述需要解Navier-Stokes方程，即一组非线性偏微分方程组。Navier-Stokes方程的复杂性使得它们在现实乐器中的应用需要一种计算解，这在现有的高性能并行计算机上是可行的。这个项目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获得各种管乐器的纳维尔-斯托克斯方程的解。这些计算研究将与实验测量相辅相成，旨在测试对建模结果的具体定性和定量预测，从而对这些工具产生新的见解。PI还将为参加奥本大学推广计划的K-12教师和学生开发声学和乐器教学模块。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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. Dr. Giordano will use advanced computational methods to study the fluid dynamics of air inside and around a variety of 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 wind instruments. An integral component of this project will be the comparison of the computational results with experiments performed with real instruments, to test and validate the computational findings. 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 and experimental methods needed to tackle a wide range of problems in science and engineering. 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. The complexity of the Navier-Stokes equations is such that their application to realistic musical instruments demands a computational solution, which is now feasible with available high performance parallel computers. 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. The PI will also develop instructional modules on acoustics and musical instruments for K-12 teachers and students who participate in outreach programs at Auburn University.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.