On the Accuracy of Harmonic Methods and a New Similarity Rule for Unsteady Transonic Flow

摘要

This paper explores the use of harmonic methods for the solution of unsteady, transonic flow. A steady harmonic approach is used for which perturbations are said to be small in comparison to the mean flow. By studying the scaling laws of the flow, the range of accuracy for each method is established. This accuracy range is important when assessing the validity of each method in handling varied levels of unsteadiness. Also a new similarity rule, which can be used to quantify the practicality of using a particular method, is found for the unsteady, transonic, quasi-one-dimensional nozzle. A non-linear, time-accurate Euler method is used to form a baseline solution for comparing each harmonic method.