| Summary: | 碩士 === 國立中興大學 === 應用數學系所 === 99 === The lid-driven cavity problem has been studied theoretically and experimentally for decades. In this study, the bifurcation phenomenon of rectangular two-sided liddriven cavity flow with various aspect ratios is explored via continuation method for the antiparallel motion and the parallel motion of two facing walls. For antiparallel motion, the upper and the bottom walls of the rectangular cavity move simultaneously in opposite directions with constant velocities while these two walls both move to the right for parallel motion. The antiparallel motion with aspect ratios from 1.0 to 2.0 and Reynolds numbers below 7500 and the parallel motion with aspect ratios from 0.54 to 1.0 and Reynolds numbers below 13000 are numerically simulated.
Comprehensive bifurcation diagrams of the cavity flow for both cases are obtained and linear stability analysis is performed to identify the nature of the various flow solutions. Furthermore, five different types of stable flow patterns for antiparallel motion and two different types for parallel motion are identified, and some critical Reynolds numbers at which the solution curve bifurcates are predicted. The flow patterns are highly dependent upon the aspect ratio of the cavity and upon the velocities of the moving walls. Not only flow patterns but also bifurcation diagrams changes tremendously around certain critical aspect ratios. According to the values of aspect ratio, there are two types of bifurcation diagrams for antiparallel motion whereas for parallel motion, bifurcation diagrams can be classified into four categories. Meanwhile, the various existent regions of stable flow patterns for antiparallel and parallel motion are recognized.
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