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REVIEW OF THEORETICAL ANALYSES OF ARC HEATING IN A TUBE,
AEROSPACE RESEARCH LABS OFFICE OF AEROSPACE RESEARCH WRIGHT-PATTERSON AFB OHIO
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The analytical methods utilized to compute the mutual interaction between a d.c. arc and a gas flow passing concurrently through a duct are reviewed and critically discussed. The numerous approximate and exact solutions for the fully-developed flow are presented in tabular form for reference purposes. Recent methods for solving the inlet flow problem are discussed, including the use of approximate laminar boundary layer methods and the exact numerical method. A new approximate solution is presented for an arc whose boundary is a paraboloid of revolution the energy equation then reduces to a hypergeometric form. Evidence is presented showing that the results of computations for d.c. arcs may be in reasonable agreement with experimental data, notably the integrated parameters such as arc voltage, the development length, etc. The existing methods for describing similar situations, but with a.c. arcs are also reviewed. It is pointed out that one might expect an oscillatory coupling between the flow and the power input at certain frequencies, resulting in resonances and possibly standing waves in the tube. Certain open problems concerned with the interaction of an arc and a coaxial gas flow are presented in conclusion. Author
APPROVED FOR PUBLIC RELEASE