Electronic Thesis and Dissertation Repository


Master of Engineering Science


Mechanical and Materials Engineering


Dr. Jerzy Maciej Floryan


A spectral algorithm based on the immersed boundary conditions (IBC) concept has been developed for the analysis of flows in channels bounded by vibrating walls. The vibrations take the form of travelling waves of arbitrary profile. The algorithm uses a fixed computational domain with the flow domain immersed in its interior. Boundary conditions enter the algorithm in the form of constraints. The spatial discretization uses a Fourier expansion in the stream-wise direction and a Chebyshev expansion in the wall-normal direction. Use of the Galileo transformation converts the unsteady problem into a steady one. An efficient solver which takes advantage of the structure of the coefficient matrix has been used. It is demonstrated that the method can be extended to more extreme geometries using the over-determined formulation. Various tests confirm the spectral accuracy of the algorithm. Pressure losses in these types of channels have been analyzed. Mechanisms of drag generation have been studied. Analytical solutions have been determined in the limit of long wavelength waves and small amplitude waves in order to simplify identification of these mechanisms. The numerical algorithm has also been validated with the help of analytical solutions. Detailed analyses of different cases, i.e. wave propagation along one wall and both walls have been carried out. Different wave profiles have been considered in order to find forms of waves which minimize pressure losses in vibrating channels. The results show dependence of the pressure losses on the phase speed of the waves, with the waves propagating in the downstream direction reducing the pressure gradient required to maintain a fixed flow rate. A drag increase is observed when the waves propagate with a phase speed similar to the flow velocity.