極音速流經二維圓柱體之數值模擬

Numerical Simulation of the Hypersonic Flow Passing over a Two-Dimension Circular Cylinder

謝勝己(Sheng-Jii Hsieh) ； 包舜華(Shun-Hua Pao)

《中國航空太空學會學刊》 30卷2期 (1998/06) Pp. 131-137

https://doi.org/10.6124/TAASRC.199806_30(2).04

摘要

本文係以數值方法模擬真實氣體流經二維圓柱體的流場，探討極音速流的高溫化學熱分解現象。其數值計算是解fully Navier-Stokes方程式，採用有限體積之面nimod TVD methed。在時間積分上採用Beam and Warming的近似分解法，並取二階之時間與空間準確度。紊流黏度則採用Baldwin and Lomax的紊流模型。計算時，假設高溫氣體已達化學熱分解平衡的流場(equilibrium flow field)，氣體溫度的修正採用Tannehill和Mugge的曲線調適法，而氣體比熱比值的修正則取自Hansen的熱力性質表。
在流場的模擬分析，首先計算兩種極音速流流過二維圓柱的流動問題，來確定數值模擬程式的正確性。最後進而計算模擬(M(下標 ∞)=8.0）極音速流流過二維等溫壁面的流場問題。圓柱壁面爲300K，而流動雷諾數Re(下標 ∞)則分別爲10^5、10^6以及10^7等三種情形以表示圓柱體半徑與熱傳的關係。計算結果顯示雷諾數爲10^7的流場在圓柱表面的熱通量約爲雷諾數10^6流場的12%，而雷諾數10^6的流場在圓柱表面的熱通量約爲雷諾數10^5流場的16%。

關鍵字

計算流體力學 ； 高溫氣體動力學 ； 極音速流

並列摘要

To investigate the hypersonic flow field of the real gas passing over a circular cylinder, the fully Navier-Stokes eqation is solved for the numerical simulation. The minimod total variation diminishion (TVD) algorithm is applied in the scheme with linearized conservative implicit (LCI) form, which was constructed in a finite-volume fashion. The approximate factorization of Beam and Warming was employed to enhance numerical efficiency. Besides, Baldwin and Lomax turbulence model is adopted for the determination of the turbulent viscosity.
In the high temperature real gas flow computation, equilibrium flow is assumed and high temperature effect is corrected. The Tannehill and Mugge curve fitting is used for the temperature correction, and the Hansen high- temperature gas property tables are employed to correct the gas specific heat ratio and the sonic speed iii the flow computions.
Five cases of numerical simulations for low-hypersonic adiabatic flow (M(subscript ∞) = 4.6, Re(subscript ∞)= 10^4); high-hypersonic adiabatic flow (M(subscript ∞)= 8., Re(subscript ∞) = 10^); and three high-hypersonic diabatic flows (M(subscript ∞), =8., Re(subscript ∞)= 10^5 10^6; and 10^7)with wall temperature kept at 300K are computed. It is found that, for the first two adiabatic cases, the numerical results of the flow pressure, temperatur and density distributions do show their satisfaction with the existing data. For the last three cases of diabatic flows at M(subscript ∞) = 8., the results show that the surface heat flux on the cylinder surface at Re(subscript ∞) =10^7 is only about 12% of that at Re(subscript ∞) =10^6, and the surface heat flux at Re(subscript ∞)=10^6 is only about 16% of that at Re(subscript ∞)=10^5. These results suggest that the heat flux is smaller for larger blunt nose body in the hypersonic flight.

並列關鍵字

CFD ； High-Temperature Gasdynamics ； Hypersonic Flows