the implementation of a time domain impedance boundary condition

Open Access
Suo, Qiuling
Graduate Program:
Aerospace Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
August 06, 2015
Committee Members:
  • Philip John Morris, Thesis Advisor
  • time domain impedance boundary condition
  • absorbing boundary
  • porous airfoil
Trailing edge noise is an important source of airframe noise. It is mainly caused by the turbulent pressure fluctuations passing an edge discontinuity. A promising passive modification for noise reduction is to use porous or partly porous airfoils. Some of the numerical studies of the porous airfoils focus on describing the complete phenomenon. The flow inside the porous region is investigated separately from the outside flow field. However, this is often computationally demanding and time consuming. For engineering purposes, a gross description of the effects of the impedance materials on incident acoustic waves is preferred. The method of time-domain impedance boundary condition is attractive to study noise scattering of absorbing surfaces. The acoustic impedance is used to describe the properties of an absorbing material. It is defined in the frequency domain as the ratio of the acoustic pressure to the acoustic velocity normal to the porous or impedance surface. Most classical impedance models were obtained in the frequency domain, and to obtain a time domain impedance boundary condition is not straightforward. In this thesis, a three-parameter model based on the mass-spring-damper system is adopted. It is verified to have a stable solution. The key to the implementation of this model is to use a ghost point outside the computational domain. This ensures that the boundary points satisfy both the discretized Euler equations and the absorbing boundary condition. Numerical results for the normal-incidence impedance tube problems show a good agreement with the analytical results. The time domain impedance boundary condition has also been developed into a two-dimensional form. An initial example problem is a Gaussian pressure pulse propagating in a uniform Cartesian grid. After that, the simulation is modified into the curvilinear coordinates to simulate the acoustic scattering around a circular cylinder. The results qualitatively show that the absorbing boundaries do reduce the amplitude of the reflected pulse. Having demonstrated simulations for a curved surface, the time domain impedance boundary condition is applied to an impedance-treated airfoil. This code could be used to find a better design of the geometry of the porous trailing edge, and to provide a better choice of the properties of the impedance.