On The Matching Of Solutions For Unsteady Transonic Nozzle Flows

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).

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The first Symposium Transsonicum took pl.ace in Aachen thirteen years ago during a period of decreasing governmental. and industrial. support for transonic flow research. Since then, there has been a strong revival. in interest in transonic flow research so that the number of partici pants at the second symposium remained about the same as at the first even in spite of tight financial. means and Limited governmental. support. During both meetings the number of participants reached the upper Limit of the number desirabl.e for such a symposium. Participants came from aU over the worl.d and there was a weU bal.anced distribution of participants from aU countries interested in transonic flow research. The discussions - mostLy conducted in EngLish - were stimul.ating and there was a great deal. of interest in the l.ectures as was shown by the good attendance even during the l.ast session on Saturday morning.