scholarly journals The impedance boundary condition for acoustics in swirling ducted flow

2018 ◽  
Vol 849 ◽  
pp. 645-675 ◽  
Author(s):  
Vianney Masson ◽  
James R. Mathews ◽  
Stéphane Moreau ◽  
Hélène Posson ◽  
Edward J. Brambley
Keyword(s):  
Boundary Condition ◽  
Surface Waves ◽  
Swirling Flow ◽  
Swirling Flows ◽  
Impedance Boundary Condition ◽  
Mean Flow ◽  
Thin Boundary Layer ◽  
Impedance Boundary ◽  
Unstable Surface ◽  
The Stability

The acoustics of a straight annular lined duct containing a swirling mean flow is considered. The classical Ingard–Myers impedance boundary condition is shown not to be correct for swirling flow. By considering behaviour within the thin boundary layers at the duct walls, the correct impedance boundary condition for an infinitely thin boundary layer with swirl is derived, which reduces to the Ingard–Myers condition when the swirl is set to zero. The correct boundary condition contains a spring-like term due to centrifugal acceleration at the walls, and consequently has a different sign at the inner (hub) and outer (tip) walls. Examples are given for mean flows relevant to the interstage region of aeroengines. Surface waves in swirling flows are also considered, and are shown to obey a more complicated dispersion relation than for non-swirling flows. The stability of the surface waves is also investigated, and as in the non-swirling case, one unstable surface wave per wall is found.

DIFFRACTION BY AN IMPEDANCE HALF-PLANE IN AN ANISOTROPIC PLASMA

1966 ◽  
Vol 44 (11) ◽  
pp. 2915-2925 ◽  
Author(s):  
R. W. Breithaupt
Keyword(s):  
Boundary Condition ◽  
Surface Waves ◽  
Half Plane ◽  
Incident Wave ◽  
Incident Field ◽  
Anisotropic Plasma ◽  
Permittivity Tensor ◽  
Impedance Boundary Condition ◽  
Magnetostatic Field ◽  
Impedance Boundary

The problem solved previously by Jull (1964) for a perfectly conducting half-plane is extended to the case of an impedance half-plane. As assumed by Jull, the direction of the incident wave is normal to both the magnetostatic field and the diffracting edge. The plasma is characterized by a permittivity tensor; and only the TM incident field is considered, as the anisotropy does not affect an incident TE wave. The impedance boundary condition is found to introduce unidirectional surface waves propagating at some angle into or away from the surface, as well as the usual radiated far fields.

Control-Oriented Methods for Turbomachinery Noise Simulation

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Alex Siu Hong Lau ◽  
Siyang Zhong ◽  
Xun Huang
Keyword(s):  
Stability Analysis ◽  
Time Domain ◽  
Sound Propagation ◽  
Impedance Boundary Condition ◽  
Generalized Function ◽  
Mean Flow ◽  
Impedance Boundary ◽  
Analysis And Design ◽  
Hopf Method ◽  
The Stability

This paper presents an innovative stability analysis and design approach for time-domain impedance boundary conditions to simulate noise propagation and radiation from a lined turbomachinery duct in the presence of a mean flow. A control-oriented model is developed for the stability analysis of the impedance boundary condition by using generalized function at the lining surface. The mean flow effect and sound propagation are considered in the model as well. Then, the numerical stability issue is analyzed by using the Bode plots before stabilized accordingly by employing the phase lead compensator method, which results in a rational transfer function. Finally, the corresponding time-domain implementation is achieved by using the so-called controllable canonical form rather than an inconvenient convolution operation. The performance of the current proposed approach is first validated in an in-duct propagation case by comparing to analytical solutions obtained by employing the Wiener–Hopf method and then demonstrated in a couple of duct acoustic problems with representative turbomachinery setups. The innovative cross-disciplinary nature of the current proposed approach can shed light on impedance problems and is very useful to time-domain acoustic simulations for turbomachinery applications.

A METHOD FOR THE TREATMENT OF A SLOPING SEA BOTTOM IN THE PARABOLIC APPROXIMATION

1996 ◽  
Vol 04 (01) ◽  
pp. 89-100 ◽  
Author(s):  
J. S. PAPADAKIS ◽  
B. PELLONI
Keyword(s):  
Boundary Condition ◽  
Helmholtz Equation ◽  
Pressure Field ◽  
Impedance Boundary Condition ◽  
Parabolic Approximation ◽  
Impedance Boundary ◽  
Local Boundary ◽  
Sea Bottom ◽  
Local Boundary Condition ◽  
Non Local

The impedance boundary condition for the parabolic approximation is derived in the case of a sea bottom profile sloping at a constant angle, as a non-local boundary condition imposed exactly at the interface. This condition is integrated into the IFD code for the numerical computation of the pressure field and implemented to test its accuracy in some benchmark cases, for which the backscattered field is negligible. It is shown that by avoiding the sloping interface, the results obtained are closer to the benchmark results given by normal mode codes solving the full Helmholtz equation, such as the 2-way COUPLE code, than those of the standard IFD or other 1-way codes, at least for problems that do not have significant backscattering effects.

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