Inviscid Unsteady Non Linear Internal Transonic Flow

Certain topics on transonic flow theory and on numerical truncation errors have been investigated. In transonic flow theory the extension of the transonic perturbation method to include flows where shock waves vanish and the development of the technique to treat separated flows was undertaken with satisfactory results. Two other topics that were investigated concerned the application of perturbation theory to accelerate convergence of numerical solutions to predict potential flow. Finally, for transonic flow, the development of a 'potential-like' theory to more closely approximate the Euler equations was undertaken. A non-linear truncation error analysis was performed on certain Euler equation algorithms to develop corrections for the solution. An outcome of this work was the derivation of a criteria for use in adaptive mesh techniques. (Author).

Masters Theses in the Pure and Applied Sciences was first conceived, published, and dis· seminated by the Center for Information and Numerical Data Analysis and Synthesis (CINDAS) *at Purdue University in 1957, starting its coverage of theses with the academic year 1955. Beginning with Volume 13, the printing and dissemination phases of the ac· tivity were transferred to University Microfilms/Xerox of Ann Arbor, Michigan, with the thought that such an arrangement would be more beneficial to the academic and general scientific and technical community. After five years of this joint undertaking we had concluded that it was in the interest of all concerned if the printing and distribution of the volume were handled by an international publishing house to assure improved service and broader dissemination. Hence, starting with Volume 18, Masters Theses in the Pure and Applied Sciences has been disseminated on a worldwide basis by Plenum Publishing Corporation of New York, and in the same year the coverage was broadened to include Canadian universities. All back issues can also be ordered from Plenum. We have reported in Volume 20 (thesis year 1975) a total of 10,374 theses titles from 28 Canadian and 239 United States universities. We are sure that this broader base for theses titles reported will greatly enhance the value of this important annual reference work. The organization of Volume 20 is identical to that of past years. It consists of theses titles arranged by discipline and by university within each discipline.

Many solutions have been presented for two dimensional transonic nozzle flows, with several different methods being represented. Two of the more interesting of these solutions are those presented by Tomotika and Tamada (1950) and Szaniawski (1965). However, it has not been made clear under what conditions either solution is valid. It is the purpose of the paper using the methods of matched asymptotic expansions, to derive the Szaniawski power series systematically and to show that this solution should be considered as an outer solution which may not be uniformly valid as the throat is approached. The inner throat region is governed by the nonlinear transonic equations which admit as one class of solutions, similarity solutions. The analysis is performed using the general non-steady inviscid equations of motion, with the steady flow results being derivable as a special case. (Modified author abstract).