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

本研究的目的是首先发展一种分析非定常跨音速流动的数值算法，特别是一种新的有限差分格式，不仅能精确地模拟激波，而且能精确地模拟非定常尾流和喷流，其次发展一个计算机图形系统，我们称之为NS（Navier-Stokes）模拟器，用于制作由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和录像系统组成，录像系统将图形数据存储到录像带中。本文介绍了所研制的NS模拟器的概况和应用情况，并已在JSME杂志上发表。本文计算了超音速压气机叶栅和跨音速涡轮机静/转子叶栅的二维非定常流场，并给出了相应的动画制作过程.在去年开发的MUSCL型有限差分格式进一步扩展到高阶TVD格式，它具有四阶精度的空间，通过采用一个简单的紧凑项。该格式的显著优点是通过提高空间精度，可以得到较弱的不连续性，如滑移线和激波。该格式在时间上采用了二阶非定常算法，大大提高了非定常尾迹、涡及其与激波相互作用的计算精度。3）将上述格式应用到NS模拟器中，并对已有格式计算的相同算例进行了模拟。最后，以动画形式存储的结果表明，非定常激波和涡之间的相互作用可以比现有的格式更精确地模拟。我们计划在罗马举行的第13届流体动力学数值方法国际会议和第28届AIAA/SAE/ASME/ASEE联合推进会议上介绍这些结果。

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.