Date of Award
Summer 2001
Document Type
Thesis - Restricted
Degree Name
Master of Science (MS)
Department
Mechanical Engineering
First Advisor
Majdalani, Joseph
Second Advisor
Dawson, Christopher A.
Third Advisor
Gaggioli, Richard A.
Abstract
Due to their broad applications, studies of porous channel flows with moving boundaries have become a popular topic in fluid mechanics. Due the complexity and nonlinearity of resulting equations, most past investigations have retied on numerical or experimental simulations. Evidently, analytical solutions can be very useful in providing a complete physical description of the problem. They can also help investigators gain a better understanding of the flow behavior depending on its physical attributes. In this thesis, the incompressible laminar flow is considered inside a porous channel with expanding or contracting walls. The main objective is to provide analytical solutions that are valid over different ranges of permeation and/or expansion/contraction rates. To define the geometry, we assume the channel's head-end to be closed by a compliant membrane while the downstream end is left fully unobstructed. For symmetric injection or suction along the porous and uniformly expanding or contracting walls, the Navier-Stokes equations are reduced to a single, nonlinear, ordinary differential equation with similarity transformations in both time and space. From this equation the characteristic flow function is obtained both numerically and asymptotically. For different magnitudes of the crossflow Reynolds number, different asymptotic expansion methods are used. For small injection and suction, double parameter perturbations are employed. For moderate to large injection, matched asymptotic expansions are used and both the outer and inner solutions are constructed. For moderate to large suction, regular perturbations are used after transforming the governing equation to a more suitable form. After the characteristic flow function is obtained, the attributes of the mean flow can be fully explored. To that end, the normal and axial velocities, the flow streamlines, the pressure distribution in both normal and axial directions, the shear stress in the flow field, and other flow features, are discussed and compared based on the numerical and analytical solutions. Thus, by varying the crossflow Reynolds number and the wall expansion ratio, one is able to elucidate the solution character while gaining a deeper understanding of the flow behavior in a channel that combines the effects of wall motion and permeability.
Recommended Citation
Zhou, Chong, "Analytical Solutions for Injection Or Suction Driven Channel Flows with Expanding or Contracting Walls" (2001). Master's Theses (1922-2009) Access restricted to Marquette Campus. 4381.
https://epublications.marquette.edu/theses/4381