Abstract
Vibration of flexible panel induced by flow and acoustic processes in a duct can be used for silencer design, but it may conversely generate noise if structural instability is induced. Therefore, a complete understanding of fluid–structure interaction is important for effective noise reduction. A new time-domain numerical methodology has been developed for the calculation of the nonlinear fluid–structure interaction of an excited panel in internal viscous flow. This paper reports its validation with two experiments. The first aims to validate that the methodology is able to capture flow-induced structural instability and its acoustic radiation. The second one is to show that the methodology captures the aeroacoustic–structural interaction in a low-frequency silencer and its response correctly. The importance of inclusion of viscous effect in both cases is also discussed.
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Abbreviations
- C :
-
Structural damping coefficient
- D :
-
Bending stiffness
- E :
-
Total energy
- \(E_p\) :
-
Modulus of elasticity
- \(\hat{H}\) :
-
Duct width and cavity height
- \(K_p\) :
-
Stiffness of foundation
- \(L_p\) :
-
Panel length
- M :
-
Mach number
- \(N_x\) :
-
Internal tensile stress of panel
- Pr :
-
Prandtl number
- \(\hat{R}\) :
-
The specific gas constant
- Re :
-
Reynolds number
- S :
-
Duct cross-sectional area
- T :
-
Temperature
- \(T_x\) :
-
External tensile stress of panel
- TL :
-
Transmission loss
- \(\hat{U}\) :
-
Inlet mean flow speed
- W :
-
Acoustic power
- a :
-
Characteristic dimension of a duct cross section
- \(c_{\textit{0}}\) :
-
Speed of sound
- dx :
-
Grid size in x-direction
- dy :
-
Grid size in y-direction
- f :
-
Frequency
- \(h_p\) :
-
Panel thickness
- k :
-
Wave number
- l :
-
Size of the fluid volume in normal direction with panel deflection
- \(l''\) :
-
End correction
- \(l_i\) :
-
Dimensions of duct in three directions, \(i=1\), 2, and 3
- \(n_i\) :
-
Mode numbers along three directions, \(i=1\), 2, and 3
- p :
-
Pressure
- \(p_A\) :
-
Amplitude of incident wave
- \(p_{ex}\) :
-
Net pressure exerted on panel
- \(q_{x}\) :
-
Heat flux in x-direction
- \(q_{y}\) :
-
Heat flux in y-direction
- t :
-
Time
- \(t_{\textit{1}}\) :
-
Time of one period
- u :
-
Fluid velocity in x-direction
- \(\hat{u}_{\textit{0}}\) :
-
The reference velocity
- v :
-
Fluid velocity in y-direction
- \(v_\eta \) :
-
Fluid velocity in \(\eta \)-direction
- \(v_\xi \) :
-
Fluid velocity in \(\xi \)-direction
- w :
-
Panel displacement
- \(\dot{w}\) :
-
Panel velocity
- \(\ddot{w}\) :
-
Panel acceleration
- \(\gamma \) :
-
The specific heat ratio
- \(\delta \) :
-
Size of the fluid volume in normal direction without panel deflection
- \(\eta \) :
-
Normal direction of the undeflected panel
- \(\theta \) :
-
Phase
- \(\mu \) :
-
Viscosity
- \(\xi \) :
-
Tangential direction of the undeflected panel
- \(\rho \) :
-
Density of fluid
- \(\rho _p\) :
-
Density of panel
- lface :
-
Lower fluid–panel interface
- lower :
-
Fluid element beneath panel
- uface :
-
Upper fluid–panel interface
- upper :
-
Fluid element above panel
- \(\hat{~}\) :
-
Dimensional quantities
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Acknowledgements
The authors gratefully acknowledge the support given by the Research Grants Council of Hong Kong SAR Government under Grant Nos. A-PolyU503/15 and AoE/P-02/12.
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Fan, H.K.H., Lam, G.C.Y., Leung, R.C.K. (2019). Numerical Study of Nonlinear Fluid–Structure Interaction of an Excited Panel in Viscous Flow. In: Ciappi, E., et al. Flinovia—Flow Induced Noise and Vibration Issues and Aspects-II. FLINOVIA 2017. Springer, Cham. https://doi.org/10.1007/978-3-319-76780-2_16
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DOI: https://doi.org/10.1007/978-3-319-76780-2_16
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