The Development of A NS Simulator for Analyzing the Unsteady Transonic Flow

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The purposes of the present research are first to develop a numerical algorithm for analyzing unsteady transonic flows, especially a new finite-difference scheme for simulating not only shocks but unsteady wakes and jets accurately, and next to develop a computer graphics system, we named Navier-Stokes (NS) simulator, for making the animation of the unsteady flow calculated by the above numerical algorithm. This system is composed of a Graphic Work Station (GWS) and the video system to memorize the graphic data into the video tape.As a final report, we can briefly summarize this research as follows.1. The brief of the developed NS simulator and the applications were reported into the Trans. JSME. In this report, unsteady 2-D flows of a supersonic compressor cascade and a transonic turbine stator/rotor cascade were calculated and the procedure of making their animations were also reported.2. The MUSCL type finite-difference scheme developed in the last year was furthermore extended to a higher-order TVD scheme, which had fourth-order accuracy in space, by adopting a simple compact term. The distinctive advantages of using this scheme is that it obtains rather weak discontinuities, for example slip lines, as well as shocks completely by improving spatial accuracy. Also this scheme with the second-order accurate unsteady algorithm in time enable us to improve the accuracy of unsteady wake, vortices and their interaction with shocks dramatically.3) The above scheme was applied into the present NS simulator and the same examples already calculated by the existing scheme were simulated. Finally the results memorized as animations show that the interaction between unsteady shocks and vortices can be simulated more sharply than the existing scheme.We plan to present these results at the 13th Int. Conf. on Numerical Method in Fluid Dynamics, Roma, and the 28th AIAA/SAE/ASME/ASEE Joint Propulsion Conf.