A Numerical Analysis of Pipe Flow Stability.
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
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Standard theoretical methods of analysis which work well for seemingly more complex problems fail to predict the experimentally observed instability of fully developed, incompressible pipe flow at any Reynolds number. Past research by Harrison and Arnold on the stability of pipe flow yielded erroneous results due to errors in the setup of the problem and formulation of the boundary conditions at the axis. A revised theory with particular attention to the rather complex boundary conditions at the axis has recently been developed. Improved finite differencing techniques with consistent fourth order truncation error were also used to approximate the governing differential equations. Numerical results for angular wave numbers zero and six show that the flow is stable at all Reynolds numbers. Results for angular wave number one contain instabilities at all Reynolds numbers for small values of the axial wave number. These results are tabulated, plotted, and discussed in detail in this paper. Author
- Fluid Mechanics