Vortices on Sound Generation and Dissipation in Musical Flue Instruments

Musical flue instruments such as the pipe organ and flute mainly consist of the acoustic pipe resonance and the jet impinging against the pipe edge. The edge tone is used to be considered as the energy source coupling to the pipe resonance. However, jet-drive models describing the complex jet/pipe interaction were proposed in the late 1960s. Such models were more developed and then improved to the discrete-vortex model and vortex-layer model by introducing fluid-dynamical viewpoint, particularly vortex sound theory on acoustic energy generation and dissipation. Generally, the discrete-vortex model is well applied to thick jets, while the jet-drive model and the vortex-layer model are valid to thin jets used in most flue instruments. The acoustically induced vortex (acoustic vortex) is observed near the amplitude saturation with the aid of flow visualization and is regarded as the final sound dissipation agent. On the other hand, vortex layers consisting of very small vortices along both sides of the jet are visualized by the phase-locked PIV and considered to generate the acceleration unbalance between both vortex layers that induces the jet wavy motion coupled with the pipe resonance. Vortices from the jet visualized by direct numerical simulations are briefly discussed.

Discrete Vortex Modeling of a Flapping Foil Energy Harvester With LEV Shedding Criterion

The energy harvesting performance of a flapping airfoil is studied through discrete vortex model. Results are obtained for a thin flat airfoil that undergoes a sinusoidal flapping motion for reduced frequencies of k = fC/U∞ = 0.06–0.16 where f is the heaving frequency of the foil, C is the chord length and U∞ is the freestream velocity. The airfoil pitches about the mid-chord and the heaving and pitching amplitudes of the airfoil are h0 = 0.5C and θ0 = 70° respectively, as these numbers have been shown to give optimal energy harvesting results for a rigid airfoil. The study applies a panel-based discrete vortex model that incorporates a leading edge suction parameter criterion to understand the flow behavior around the airfoil. The leading edge suction parameter is found from 2D CFD simulations (Navier-Stokes equations solved in Fluent) for all K values. A correlation between the critical leading edge suction parameter and reduced frequency is found from the identified critical LESP values. An empirical trailing edge separation correction is also applied to the transient force results since flow separation at the trailing edge is anticipated. The parameters of interest from the model are transient distributions of force, power output, and overall efficiency. Model results are then validated against 2D CFD simulations. The effect of reduced frequency on power production and overall efficiency is finally studied to identify the optimal reduced frequency for energy harvesting applications.

Image Singularity System to Represent Two Circular Cylinders of Different Diameter

The singularity system to represent two circular cylinders poised under different ambient flow fields is considered in the present research. The singularity system, composed of a series of singularities, has to be truncated for numerical calculations. A rational criterion to determine how many terms of this series should be retained to maintain the prescribed accuracy is provided through analysis of the converging property of the series. A particular emphasis is put on how to deal with the discrete vortex model of a boundary layer, this possibility being the basis for the development of a tool to simulate vortex shedding from a structure composed of two circular cylinders. The principle in obtaining the present singularity system can be applied to more-than-two-cylinders structures. Only the series becomes more complex with an increase in the number of cylinders. [S0098-2202(00)01704-1]