Abstract
隨著CFD技術的快速發展和高速超級電腦的問世，借助CFD進行飛行器氣動力定型設計已成趨勢，然而高速飛行體周圍流場，因涉及高雷諾數震波干涉分離流場的解析，常因紊流模式效果不彰影響設計精度。本文分別探討低雷諾數雙方程式紊流模式、ASM/k-ε雙層混合模式和低雷諾數雷諾應力紊流模式，對於穿音速流流經軸對稱隆起物、超音速流流經斜坡等震波–邊界層干涉分離流場，和超音速彈尾迴漩流場等問題進行測試，證實只有雷諾應力紊流模式可以掌握流場分離特性，雙方程式紊流模式則連震波–邊界層干涉分離流場之震波位置都無法預測，至於 ASM/k-ε雙層混合模式確實可改善壓力場震波位置的捕捉，然因近壁處使用雙方程式紊流模式，因此無法預測流場分離特性。然因雷諾應力紊流模式計算之迴漩流域較寬廣，故在重新發展流域之速度回復速率較慢。為避免不連續震波之數值震盪並維持高解析度，非線性對流項之數值通量本文採用Harten TVD計算。除此之外，以低雷諾數紊流模式取代壁函數處理壁附近流場時，因為格點變密，紊流模式非線性源項之值變大，為克服產生的數值收斂不易等問題，本文採用鬆弛法以避免裂解誤差，並引入改良過之雙共軛梯度法如CGS、Bi-CGSTAB和TFQMR等方法，配合ILU前置處理方法疊代求解大型線性矩陣，以加速收斂。測試結果發現鬆弛法因無裂解誤差，故紊流傳輸方程式不必加進鬆弛因子即可穩定收斂．若每一時步之鬆弛法僅做一次疊代，則收斂最佳之Bi-CGSTAB法其計算效益可達ADI法之2.4~5.5倍，且流場愈複雜計算效益愈顯著 。經由可壓縮混合層流場之試驗研究，發現可壓縮效應抑制紊流動能成長，因此許多研究者於可壓縮流場計算時，分別在紊流黏性消散項ε和壓力膨漲項(pressure dilation)加入可壓縮效應修正以增加計算準確性。然而對本文之彈尾流場，現有修正模式之測試效果不彰，反而更低估迴流區之速度，為改進此一缺失，在修正模式之係數中加入 V•▽ρ/(ρ｜V｜)當為過慮器(filter)，以適度表現出膨漲波和壓縮震波之特性，證實確可改善迴漩流域之紊流特性模擬結果。With the rapid advances in supercomputer，the use of CFD as adesign tool for aerospace vehicles has become popular．However，it is dependent on the turbulence modeling to accuratelysimulate the complex flows． In the present study， theperformance of k-ε model、ASM/k-ε two-layer model andReynolds stress models are examined for the shock-inducedseparated flows and supersonic base flow．The RSM yields thebest agreement in the recirculating region，but implies aninsufficient recovery of velocity during flow redeveloping．The k-ε model can not correctly capture the shock location inshock-induced separated flows．Although the ASM/k-εmodelprovides an improvement in capturing shock，the ability tosimulate the separated flowfields is restrained by the use of k-ε model in the inner layer． To avoid the spuriousoscillations and maintain high resolution across shock，theconvective terms are discretized with Harten's TVD scheme inthis study． Also，the preconditioning technique of ILU isincorporated into the relaxation solver of CGS、 Bi-CGSTAB andTFQMR to accelerate convergence． Without the factorizationerror in iterative method，the residuals of turbulent equationscan converge to lower level than AF method．The Bi-CGSTABmethod can speed up the CPU time by a factor of 2.4~5.5 ascompared to the AF method． In the study of compressible mixinglayer， additional dilational effects are usually included inthe viscous dissipation term εto improve the accuracy ofsimulation．In the base flow，It is found that original modelsoverestimate the recirculating flow region．By adding thedensity gradient term V•▽ρ/(ρ｜V｜) as a filter in thecoefficient，an alternative approach has been adopted to showthe different characteristics between the compression wave andexpansion wave．The results show a good improvement in thesimulation of turbulent flowfields．