Analysis Of Nonlinear Transonic Blockage In Unsteady Transonic Flows

The effects of unsteady modes of motion on two-dimensional transonic flows are investigated. Numerical algorithms that treat shock waves as moving discontinuities are described for nonlinear and time-linearized perturbation flows. Results for transonic flow past an NACA 64A006 airfoil experiencing harmonic motions in one of several modes are presented. (Author).

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).

This thesis explores linear and non-linear computational methods for solving unsteady flow. The eventual goal is to apply these methods to two-dimensional and three-dimensional flutter predictions. In this study the quasi-one-dimensional nozzle is used as a framework for understanding these methods and their limitations. Subsonic and transonic cases are explored as the back-pressure is forced to oscillate with known amplitude and frequency. A steady harmonic approach is used to solve this unsteady problem for which perturbations are said to be small in comparison to the mean flow. The use of a linearized Euler equations (LEE) scheme is good at capturing the flow characteristics but is limited by accuracy to relatively small amplitude perturbations. The introduction of time-averaged second-order terms in the Non-Linear Harmonic (NLH) method means that a better approximation of the mean-valued solution, upon which the linearization is based, can be made. The nonlinear time-accurate Euler solutions are used for comparison and to establish the regimes of unsteadiness for which these schemes fails. The usefulness of the LEE and NLH methods lie in the gains in computational efficiency over the full equations.