*Sound generation due to unsteady motion of a cylinder*. A. Sharma and S.K. Lele. *Physics of Fluids*, 23:046102, 2011.

A two-dimensional model problem of sound generation due to prescribed unsteady starting and stopping motion of a circular cylinder is studied by the numerical solution of two-dimensional compressible Navier-Stokes equations. The unsteady flow near the cylinder surface and the sound generation and propagation are analyzed with respect to three parameters: the time scale of the startup and stopping motion, the peak Mach number (based on peak velocity and ambient speed of sound), and the Reynolds number (based on peak velocity, cylinder diameter, ambient density, and dynamic viscosity). The flow behavior is studied for fast (time scale of unsteady motion similar to acoustic time scale) or very slow startup motion. The Mach number is varied between 0.1 and 0.4 and the Reynolds number between 150 and 9500. The accuracy of unsteady flow solution is demonstrated by comparison to the experimental data. For fast startup motion, a sharp peak is observed in the drag curve during the acceleration phase of motion. We find that the dominant contribution to total drag comes from the pressure drag and the peak drag force scales with peak velocity. The startup process introduces weak shock waves in the flow, which contributes to the far-field noise. For slow startup motion, the drag curve is smoother and the drag force scales with the square of the peak velocity. For fast startup motion, the acoustic energy that propagates to the far-field scales with the square of the peak velocity, whereas for slow startup, it scales with the fourth power of the peak velocity. The amount of sound energy radiated to the far-field is found to be a small percentage of the total energy input to set up the entire motion of cylinder. An interpretation for the observed scaling relations in the numerical data is presented using different asymptotically valid reduced forms of the governing equations.

`@ARTICLE { lelesharma2011sound,`

TITLE = { Sound generation due to unsteady motion of a cylinder },

AUTHOR = { A. Sharma and S.K. Lele },

JOURNAL = { Physics of Fluids },

VOLUME = { 23 },

PAGES = { 046102 },

YEAR = { 2011 },

ABSTRACT = { A two-dimensional model problem of sound generation due to prescribed unsteady starting and stopping motion of a circular cylinder is studied by the numerical solution of two-dimensional compressible Navier-Stokes equations. The unsteady flow near the cylinder surface and the sound generation and propagation are analyzed with respect to three parameters: the time scale of the startup and stopping motion, the peak Mach number (based on peak velocity and ambient speed of sound), and the Reynolds number (based on peak velocity, cylinder diameter, ambient density, and dynamic viscosity). The flow behavior is studied for fast (time scale of unsteady motion similar to acoustic time scale) or very slow startup motion. The Mach number is varied between 0.1 and 0.4 and the Reynolds number between 150 and 9500. The accuracy of unsteady flow solution is demonstrated by comparison to the experimental data. For fast startup motion, a sharp peak is observed in the drag curve during the acceleration phase of motion. We find that the dominant contribution to total drag comes from the pressure drag and the peak drag force scales with peak velocity. The startup process introduces weak shock waves in the flow, which contributes to the far-field noise. For slow startup motion, the drag curve is smoother and the drag force scales with the square of the peak velocity. For fast startup motion, the acoustic energy that propagates to the far-field scales with the square of the peak velocity, whereas for slow startup, it scales with the fourth power of the peak velocity. The amount of sound energy radiated to the far-field is found to be a small percentage of the total energy input to set up the entire motion of cylinder. An interpretation for the observed scaling relations in the numerical data is presented using different asymptotically valid reduced forms of the governing equations. },

}