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Computation of aeolian tones from twin-cylinders using immersed surface dipole sources

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Abstract

Efficient numerical method is developed for the prediction of aerodynamic noise generation and propagation in low Mach number flows such as aeolian tone noise. The proposed numerical method is based on acoustic/viscous splitting techniques of which acoustic solvers use simplified linearised Euler equations, full linearised Euler equations and nonlinear perturbation equations as acoustic governing equations. All of acoustic equations are forced with immersed surface dipole model which is developed for the efficient computation of aerodynamic noise generation and propagation in low Mach number flows in which dipole source, originating from unsteady pressure fluctuation on a solid surface, is known to be more efficient than quadrupole sources. Multi-scale overset grid technique is also utilized to resolve the complex geometries. Initially, aeolian tone from single cylinder is considered to examine the effects that the immersed surface dipole models combined with the different acoustic governing equations have on the overall accuracy of the method. Then, the current numerical method is applied to the simulation of the aeolian tones from twin cylinders aligned perpendicularly to the mean flow and separated 3 diameters between their centers. In this configuration, symmetric vortices are shed from twin cylinders, which leads to the anti-phase of the lift dipoles and the in-phase of the drag dipoles. Due to these phase differences, the directivity of the fluctuating pressure from the lift dipoles shows the comparable magnitude with that from the drag dipoles at 10 diameters apart from the origin. However, the directivity at 100 diameters shows that the lift-dipole originated noise has larger magnitude than, but still comparable to, that of the drag-dipole one. Comparison of the numerical results with and without mean flow effects on the acoustic wave emphasizes the effects of the sheared background flows around the cylinders on the propagating acoustic waves, which is not generally considered by the classic acoustic analogy methods. Through the comparison of the results using the immersed surface dipole models with those using point sources, it is demonstrated that the current methods can allow for the complex interactions between the acoustic wave and the solid wall and the effects of the mean flow on the acoustic waves.

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Abbreviations

c :

Speed of sound

C d :

Coefficient of drag

C i :

Coefficient of lift

D :

Diameter of cylinder

e :

total energy

e 0 :

e+1/2·v 2, stagnation total energy

h :

Enthalpy

h 0 :

h+1/2·v2, stagnation total enthalpy

I :

Turbulence intensity

k :

Turbulent kinetic energy

L :

Turbulence length scale

ρ:

Static pressure

P :

\(p - \mathop {\lim }\limits_{T \to \infty } \int_{ - T}^T {pdt/T} \), fluctuating surface pressure

Re :

u ∞ d/v, Reynolds number

s :

Entropy

S :

Immersed dipole source vectors

St :

Df/u ∞ , Strouhal number

T :

Period of vortex shedding

t :

Time

u ∞ :

Free stream velocity

u i :

Fluid velocity in a cartesian coordinate system

X i :

Cartesian coordinate system

γ:

Ratio of specific heats, γ=1.4 for air

ν:

Kinetic viscosity

νt :

Eddy viscosity

νeff :

ν+νt, effective viscosity

ρ:

Eensity

ε:

Turbulence energy dissipation

a :

Denote the acoustical quantity

f :

Denote the viscous flow quantity

∞:

Denote the free-stream quantity

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Authors and Affiliations

  1. School of Mechanical Engineering, Pusan National University, 30, Jangjeondong, Geumjeonggu, 609-745, Pusan, Korea

    Cheolung Cheong

  2. Gas Turbine Development Team, Center for Advanced Systems Development, Corporate R&D Institute, Doosan Heavy Industries & Construction Co. Ltd., 58-4 Hwaam-Dong, Yuseong-Gu, 305-348, Daejeon, Korea

    Jewook Ryu

  3. School of Mechanical and Aerospace Engineering, Seoul National University, Shinrimdong, Gwanakgu, 151-742, Seoul, Korea

    Soogab Lee

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  1. Cheolung Cheong
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Correspondence to Cheolung Cheong.

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Cheong, C., Ryu, J. & Lee, S. Computation of aeolian tones from twin-cylinders using immersed surface dipole sources. J Mech Sci Technol 20, 2292–2314 (2006). https://doi.org/10.1007/BF02916345

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