使用加權基本不震盪算則之超音速衝壓引擎流場模擬分析

Abstract

本研究基於氣體動力學之理論基礎，以可壓縮Navier-Stokes方程式為統御方程，來求解超音速燃燒衝壓引擎的流場問題。在紊流模型的選擇上使用較好計算之Spalart-Allmaras單方程式模組，此模組在壁面與邊界層附近的流場問題能得到較好的結果。數值方法部分將以加權基本不震盪算則(WENO)計算，並搭配在穩態問題中可以較快收斂的LU-SGS隱式算則來模擬。藉由加權基本不震盪算則具有高階準確性以及在不連續點能不震盪地解析出不連續數值解的特性，可以將其應用在有許多震波交互作用的超音速流場問題中。本文將使用上述之模擬方法，先與參考文獻中的燃燒室模擬與雙圓錐進氣道模擬做驗證比較，確認此方法的準確性。接著再針對一個完整的超音速燃燒衝壓引擎之流場問題，以不同的初始條件進行模擬，得到其馬赫數、密度、溫度及壓力的分佈情形，並討論其結果。結果顯示，加權基本不震盪算則不僅可以成功地模擬超音速流場問題，即便是在兩震波相當接近的情況下，也能解析出更準確的結果。

This study is based on the theory of gas dynamics and uses the Navier-Stokes equations as the governing equations to solve the fluid flow field problems of the scramjet. For the turbulent flow, we use the simple Spalart-Allmaras one equation turbulence model (S-A model) which produces better results for near wall and boundary layer flow field problems. The lower-upper symmetric Gauss-Seidel (LU-SGS) implicit scheme, whose results converge efficiently under steady state conditions, is combined with the Weighted Essentially Non-Oscillatory (WENO) scheme to construct a numerical model of the scramjet. Using the WENO scheme’s high-order accuracy and its non-oscillatory solution at discontinuous areas, we can solve supersonic flow field problems with multiple shock wave interactions. This simulation procedure is verified against two partial examples from literature to ensure its accuracy, and is then applied to a complete geometric model of a scramjet with different initial conditions for a full flow field analysis. The Mach number, density, static temperature and pressure are found and the results discussed. It is found that even when the shock waves are very close to each other, the WENO scheme produces better simulation results than other numerical approaches.