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Varieties of research on turbulent-induced noise are conducted with combinations of acoustic analogy methods and computational fluid dynamic methods to analyse efficiently and accurately. Application of FW-H acoustic analogy without turbulent noise is the most popular method due to its calculation cost. In this paper, turbulent-induced noise is predicted using RANS turbulence model and permeable FW-H method. For simplicity, noise from 2D cylinder is examined using three different methods: direct method of RANS, FW-H method without turbulent noise and permeable FW-H method which can take into account of turbulent-induced noise. Turbulent noise was well predicted using permeable FW-H method with same computational cost of original FW-H method. Also, ability of permeable FW-H method to predict highly accurate turbulent-induced noise by applying adequate permeable surface is presented. The procedure to predict turbulent- induced noise using permeable FW-H is established and its usability is shown.

Objects in motion in fluid disturb its surroundings to produce noise. Such noise can be predicted using Kirchhoff formula or Acoustic analogy [

The turbulent-induced noise can be predicted correctly using DNS (Direct Numerical Simulation) method. However it is almost impossible because of high computational cost [

In this study, the use of RANS (Reynolds Averaged Navier-Stokes) turbulent model of CFD and permeable FW-H which accommodates permeable surface is shown to predict turbulent-induced noise. Direct method to directly extract perturbing pressure, FW-H method without quadruple term, and permeable FW-H which includes the effects of turbulence are compared for 2-dimensional circular cylinder. Permeable FW-H method has shown to well predict the influence of turbulent noise compared to the method without quadruple term. Moreover, it is shown that careful selection of permeable surface can result in high accuracy from permeable FW-H method.

Lighthill has introduced the wave equation of acoustic analogy having the source derived by comparing the exact equations of motion of a fluid with the equations of sound propagation in a medium at rest as follows [

Here

Curle’s analogy have expanded the Lighthill’s theory considering rigid surface (Curle, 1995), an Ffowcs Williams and Hawkings have further generalized the theory considering rigid object in arbitrary motion as follows [

Here,

Farassat’s formulation develops FW-H analogy equation into following integral forms [

Here,

Turbulent term which is represented as quadrupole source is in volume integration. Decision of the volumes in fluid around rigid body to integrate and evaluation of the integration kernel is difficult [

To analyze the circular cylinder with 20 mm diameter, total of 218,268 cells are constructed. Receiver points for acoustic analysis are place at perpendicular to the flow direction downward from the cylinder in distance of 10 mm, 70 mm. Dimensionless Wall Distance (Wall Y+) is set to lower than 1 to accurately calculate boundary layers. In addition, overall mesh takes from of C-H for better quality such as skewness and orthogonality around the cylinder.

Permeable surface (Inner-Cell) for permeable FW-H method is set to include boundary layers and 3 - 4 vortex shedding as in

Ansys FLUENT v14.5 is used for CFD calculation and also FW-H method without turbulent term and permeable FW-H with Inner-Cell boundary condition [

K − ω SST | Strouhal No. (S_{t}) |
---|---|

Experiment (Park, 2012) | 0.195 |

Experiment (Norberg, 2003) | 0.190 |

Simulations (Park, 2012) | 0.198 |

Simulations (Orselli, 2009) | 0.247 |

Result | 0.222 |

Considering the fact that the FW-H without quadruple term cannot represent the noise by the turbulence implies that the permeable FW-H method has well predicted the turbulence-induced noise. It can be stated from the result that the procedure to predict turbulent-induced noise is established. Also, it is shown that the Permeable FW-H method is robust compared to the standard FW-H method.

Here, permeable FW-H also shows good agreement toward the direct method showing the similar characteristics that of the results in air. This also represents the robustness of the permeable FW-H method.

Accurate results can be obtained from FW-H methods inside the permeable surface both in air and underwater. In

Prediction of the turbulence-induced noise around 2-dimensional circular cylinder is done by the three different methods: direct method to directly extract perturbing pressure, FW-H without quadruple term which represents the noise due to the turbulence and permeable FW-H method which includes the turbulent-induced noise.

The difference between the direct method and the FW-H without quadruple term represents the magnitude of the noise due to the turbulence. Permeable FW-H method shows good agreement with the direct method. The robustness of the permeable FW-H method is shown from different results that the permeable FW-H method can well predict the noise produced from turbulence. By reversing the normal vector of the permeable surface, the near-field prediction could improve its accuracy. In conclusion, the procedure to predict turbulent-induced noise by using the permeable FW-H method is established and its usefulness is shown.

In further studies, the selection of Inner-Cell considering not only the size of the surface but also the length and frequency of vortex shedding and turbulent-induced noise prediction in more complex geometries are considered to generalize the current procedure of predicting the turbulent-induced noise.

Woen-Sug Choi,Suk-Yoon Hong,Jee-Hun Song,Hyun-Wung Kwon,Chul-Min Jung,Tae-Gyoung Kim, (2015) Turbulent-Induced Noise around a Circular Cylinder Using Permeable FW-H Method. Journal of Applied Mathematics and Physics,03,161-165. doi: 10.4236/jamp.2015.32025