Flows in Vibrating Channels

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

Spectrally-Accurate Algorithm for Flows in 3-Dimensional Rough Channels

In this work a spectrally accurate algorithm has been developed for the simulation of three-dimensional flows bounded by rough walls. The algorithm is based on the velocity-vorticity formulation and uses the concept of Immersed Boundary Conditions (IBC) for the enforcement of the boundary conditions. The flow domain is immersed inside a fixed computational domain. The geometry of the boundaries is expressed in terms of double Fourier expansions and boundary conditions enter the algorithm in the form of constraints. The spatial discretization uses Fourier expansions in the stream-wise and span-wise directions and Chebyshev expansions in the wall-normal direction. The algorithm can use either the fixed flow rate constraint or the fixed pressure gradient constraint; a direct implementation of the former constraint is described. An efficient solver which takes advantage of the structure of the coefficient matrix has been developed. Taking the advantage of the reality conditions enhances the efficiency of the solver both in terms of memory and computational speed. It is demonstrated that the applicability of the algorithm can be extended to more extreme geometries using the over-determined formulation. Various tests confirm the spectral accuracy of the algorithm

Effects of Grooves on Drag in Laminar Channel Flow

This thesis presents the analysis of the effects of three-dimensional grooves on the flow responses in laminar channel flows. The wall topographies were expressed using the two-dimensional Fourier expansions. A spectrally accurate algorithm based on the Immersed Boundary Conditions (IBC) was used to determine the solution for the field equations and extract information about the velocity and pressure fields. The effects of grooves on the pressure losses were assessed by determining the additional pressure gradient required to maintain the same flow rate through the grooved channel as through the reference smooth channel. Effects of groove wave numbers, groove amplitudes, the relative position of the upper and lower groove systems as well as the flow Reynolds number were considered. It has been shown that it is possible to identify surface topographies that lead to the reduction of pressure losses in spite of an increase of the wetted surface area. Only topographies that show a preference for the longitudinal wave numbers are able to reduce pressure losses. The interaction of groove systems present on different channel walls affects the magnitude of drag reduction. The most effective relative positions of these systems have been identified