Date of Award
Fall 2001
Document Type
Thesis - Restricted
Degree Name
Master of Science (MS)
Department
Mechanical Engineering
Abstract
The oscillatory velocity field developed in porous channels and tubes with arbitrary levels of suction imposed at the porous surfaces is investigated. Based on the normalized pressure wave amplitude, the governing equations are linearized and split into leading-order (steady) and first-order (time-dependent) equations. The first-order set is subdivided into an acoustic, pressured-driven, wave equation, and a vortical, boundary-driven, viscous equation. Both equations are solved under the assumption that the wall suction Mach number is a small quantity. The acoustic set is solved exactly, while a solution to the vortical set is achieved using classic perturbation techniques. An accurate description of the vortical response requires the solution of a second order ordinary differential equation referred to as the separated momentum equation. Solutions to this singular double perturbation problem are achieved using the method of multiple-scales and a WKB expansion. Additionally, over limited ranges of suction, a solution is found using matched asymptotic expansions and an exact solution is formulated following a Liouville-Green transformation. The exact and asymptotic solutions are found to coincide with a numerical solution of the linearized momentum, equation. The features exhibited by the oscillatory velocity agree with conclusions drawn from the theory of periodic flows. In particular, a thin rotational layer is observed along with a small velocity overshoot near the wall. The acoustic boundary-layer is found to decrease with increases in both suction speed and oscillation frequency.
Recommended Citation
Jankowski, Todd, "Oscillatory Flows in Porous Tubes and Channels with Arbitrary Wall Suction" (2001). Master's Theses (1922-2009) Access restricted to Marquette Campus. 4852.
https://epublications.marquette.edu/theses/4852