Fluid Flow Analysis in Corrugated Curved Channels

Abstract

Fluid Flow Analysis in Corrugated Curved Channels The fluid flow in corrugated curved channels have been investigated in this thesis. Curvilinear coordinate system is used to formulate the problem. The corrugations are defined by sinusoidal wave patterns. The phase difference between the corrugations of the two boundaries is assumed arbitrarily. The flow is generated by constant pressure gradient. Two flow orientations are discussed: The flow parallel and the flow perpendicular to the corrugations of a curved channel. The parallel flow leads to a unidirectional flow problem, while the perpendicular flow leads to a bidirectional flow problem. The boundary conditions are variable in nature, and are of small perturbation to that of a smooth curved channel. The analytical solutions for the velocity field and volumetric flow rate for the two flow orientations are presented using asymptotic analysis in terms of small amplitude of the corrugations: The boundary perturbation method has been employed to deal with the complex boundary conditions. The effects the geometrical parameters specifying the curvature and the corrugations on the velocity field and volumetric flow rate have been studied. The flow control is essentially a function of these geometrical parameters, and a detailed study to optimize the flow rate in the corrugated curved channels is presented. The theoretical study is further carried over to electrically conducting fluids, and the effects of an additional body force due to applied magnetic field is investigated, to examine the coupled effects of the channel geometry in this physical situation. In the end, an analogy with the thin gap approximation for the flows in corrugated curved channels with relatively small width is also discussed. The results for curved smooth channels and straight corrugated channels are the special cases of the present studies. Overall, this study presents an innovation from the perspective of giving a first-time insight into the salient flow characteristics in corrugated curved channels for distinct flow orientations and geometrical configurations. This aspect of curved channel flows is not well explored in the literature and its understanding is rather limited. Therefore, the present research is significant in demystifying the flow characteristics in curved channels with wall unevenness or surface roughness resulting either due to imposition, or due to x defects in fabrication relating to limitations in the engineering technology. The study maybe considered as a benchmark to understanding flows in corrugated curved channels in the form of cracks, rough arteries, rough capillaries, wavy curved channels in heat exchangers, mixers and so on, where the physical and the geometrical assumptions in this study can be reasonably applied. Keywords: corrugations, wavenumber, amplitude, phase difference, radius of curvature,pressure gradient, Lorentz force, velocity, flow rate, boundary perturbation.