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

本研究的目的是首先开发一种分析跨声速非定常流动的数值算法，特别是一种不仅能精确模拟激波，而且能精确模拟非定常尾迹和喷流的新的有限差分格式。其次，开发一个计算机图形系统，我们称之为Navier-Stokes(NS)模拟器，用于制作用上述数值算法计算的非定常流动的动画。该系统由图形工作站(GWS)和将图形数据存储到录像带中的视频系统组成。向TRANS报告了NS模拟器的开发和应用情况。JSME。本文对超音速压气机叶栅和跨声速涡轮静/转子叶栅的非定常二维流动进行了数值模拟，并介绍了其动画制作过程。通过采用简单的紧致项，将过去一年发展起来的MUSCL型有限差分格式进一步扩展到在空间上具有四阶精度的高阶TVD格式。使用这种格式的显著优点是，它通过提高空间精度获得了相当弱的不连续性，例如滑移线，以及完全的冲击。该格式与时间上的二阶精度非定常算法相结合，使得非定常尾迹、旋涡及其与激波的相互作用的精度有了很大的提高。3)将上述格式应用到NS模拟器中，并对已有的算例进行了模拟。最后，以动画形式存储的结果表明，非定常激波和涡旋之间的相互作用可以比现有的方案更准确地模拟。我们计划在第13届国际会议上公布这些结果。电话会议流体力学数值方法，ROMA，第28届AIAA/SAE/ASME/ASEE联合推进会议。

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.