Sound Generation by a Turbulent Flow in Musical Instruments - Multiphysics Simulation Approach -

Total computational costs of scientific simulations are analyzed between direct numerical simulations (DNS) and multiphysics simulations (MPS) for sound generation in musical instruments. In order to produce acoustic sound by a turbulent flow in a simple recorder-like instrument, compressible fluid dynamic calculations with a low Mach number are required around the edges and the resonator of the instrument in DNS, while incompressible fluid dynamic calculations coupled with dynamics of sound propagation based on the Lighthill's acoustic analogy are used in MPS. These strategies are evaluated not only from the viewpoint of computational performances but also from the theoretical points of view as tools for scientific simulations of complicated systems.Comment: 6 pages, 10 figure files, to appear in the proceedings of HPCAsia0

Theoretical Estimation of the Acoustic Energy Generation and Absorption Caused by Jet Oscillation

We investigate the energy transfer between the fluid field and acoustic field caused by a jet driven by an acoustic particle velocity field across it, which is the key to understanding the aerodynamic sound generation of flue instruments, such as the recorder, flute, and organ pipe. Howe’s energy corollary allows us to estimate the energy transfer between these two fields. For simplicity, we consider the situation such that a free jet is driven by a uniform acoustic particle velocity field across it. We improve the semi-empirical model of the oscillating jet, i.e., exponentially growing jet model, which has been studied in the field of musical acoustics, and introduce a polynomially growing jet model so as to apply Howe’s formula to it. It is found that the relative phase between the acoustic oscillation and jet oscillation, which changes with the distance from the flue exit, determines the quantity of the energy transfer between the two fields. The acoustic energy is mainly generated in the downstream area, but it is consumed in the upstream area near the flue exit in driving the jet. This theoretical examination well explains the numerical calculation of Howe’s formula for the two-dimensional flue instrument model in our previous work [Fluid Dyn. Res. 46, 061411 (2014) ] as well as the experimental result of Yoshikawa et al. [ J. Sound Vib. 331, 2558 (2012) ]

Mode Selection Rules and Bifurcation Diagrams for Two-Delay Systems: Underlying Mechanism Controlled by Embedded Multidimensional Maps

We study mode selection rules at the first bifurcation and bifurcation diagrams for a two-delay system with a positive feedback of a long delay time t2 and with either a positive or negative feedback of a short delay time t1, i.e., 0 < t1 < t2. The mode excited by the first bifurcation changes with t1/t2, and the relevant and irrelevant conditions, which are rational numbers in t1/t2 with t1/t2 = n/m, characterize the mode selection rule; a definite subset of the rational numbers is relevant and its complement is irrelevant. In a neighborhood of a relevant condition, oscillations each with period T ≈ 2t2/m, i.e., mth-order harmonic, are excited at the first bifurcation. In a neighborhood of an irrelevant condition, twin peaks consisting of higher-order harmonics are observed. The mode selection rule markedly changes with the strength of the short delay; the relevant condition changes reflecting the change in the underlying mechanism of the bifurcation process. In this paper, we show that for each of the relevant and irrelevant conditions, the two-delay system is reduced to an m-dimensional map in the nondispersive limit, i.e., a singular perturbation limit. In terms of multidimensional maps, the first bifurcation for the relevant condition is either a pitchfork or period-doubling bifurcation, while a Hopf bifurcation is observed for the irrelevant condition. The mode selection rules together with the waveforms are explained from the analysis of the multidimensional maps. Furthermore, the global structure of transitions among attractors after the first bifurcation is approximately predicted from the analysis of the multidimensional maps

Open-architecture Implementation of Fragment Molecular Orbital Method for Peta-scale Computing

We present our perspective and goals on highperformance computing for nanoscience in accordance with the global trend toward "peta-scale computing." After reviewing our results obtained through the grid-enabled version of the fragment molecular orbital method (FMO) on the grid testbed by the Japanese Grid Project, National Research Grid Initiative (NAREGI), we show that FMO is one of the best candidates for peta-scale applications by predicting its effective performance in peta-scale computers. Finally, we introduce our new project constructing a peta-scale application in an open-architecture implementation of FMO in order to realize both goals of highperformance in peta-scale computers and extendibility to multiphysics simulations.Comment: 6 pages, 9 figures, proceedings of the 2nd IEEE/ACM international workshop on high performance computing for nano-science and technology (HPCNano06

Multi-physics Extension of OpenFMO Framework

OpenFMO framework, an open-source software (OSS) platform for Fragment Molecular Orbital (FMO) method, is extended to multi-physics simulations (MPS). After reviewing the several FMO implementations on distributed computer environments, the subsequent development planning corresponding to MPS is presented. It is discussed which should be selected as a scientific software, lightweight and reconfigurable form or large and self-contained form.Comment: 4 pages with 11 figure files, to appear in the Proceedings of ICCMSE 200

Interaction between compressible fluid and sound in a flue instrument

In order to study the generation of (aerodynamic) sound in flue instruments, we numerically apply Howe’s energy corollary for a 2D model of flue instrument. Howe’s energy corollary enables us to estimate the energy transfer between fluid flow and acoustic field. To implement it, separating the acoustic field from the fluid flow is needed. However the complete method to numerically achieve it has not been established yet. In this work, we develop an approximate method, which has been recently proposed in their experimental studies by Yoshikawa et al (2012 J. Sound Vib. 331 2558-2577) and others, and we apply it to the simulation of the model instrument. We first calculate fluid flow and acoustic oscillation simultaneously by a compressible fluid solver. Next referring to the information on the acoustic oscillation obtained we set up a pressure source on an acoustic solver and reproduce almost the same acoustic oscillation with it. Combining those results, we are able to calculate Howe’s energy corollary. The numerical result shows that the aerodynamic sound is generated from the oscillating jet rather than the vortices shed by the collision of it with the edge of the mouth opening, namely vortex shedding

Numerical Study on Acoustic Oscillations of 2D and 3D Flue Organ Pipe Like Instruments with Compressible LES

Acoustic oscillations of flue instruments are investigated numerically using compressible Large Eddy Simulation (LES). Investigating 2D and 3D models of flue instruments, we reproduce acoustic oscillations excited in the resonators as well as an important characteristic feature of flue instruments – the relation between the acoustic frequency and the jet velocity described by the semi-empirical theory developed by Cremer & Ising, Coltman and Fletcher et al. based on experimental results. Both 2D and 3D models exhibit almost the same oscillation frequency for a given jet velocity, but the acoustic oscillation as well as the jet motion is more stable in the 3D model than in the 2D model, due to less stability in 3D fluid of the rolled up eddies created by the collision of the jet with the edge, which largely disturb the jet motion and acoustic field in the 2D model. We also investigate the ratio of the amplitude of the acoustic flow through the mouth opening to the jet velocity, comparing with the experimental results and semi-empirical theory given by Hirschberg et al.