本文利用數值模擬的方法，來分析高展弦比（AR=15）轉接段對向量推力系統內流場的性質與噴嘴性能的影響。所採用的數值方法是以有限體積法採用三階上風外插與限制函數，時間積分上採用顯式三階段的兩階Runge-Kutta method，求解三維、非軸對稱、可壓縮尤拉方程式。狀態方程式以理想氣體方程式來加以描述，並假設向量推力系統壁面為絕熱條件，入口為次音速流，給定上游條件；出口為超音速流，故直接外插求得。
為驗證基本格點數量是否足夠表現流場特性，將區間內各邊上的格點數加倍，來比較格點的效應，比較結果顯示所選取格點數量足夠。以加轉接段之無偏折角噴嘴(D1N00)的結果與實驗值[1]作比較，結果顯示，此數值方法之結果與實驗之比對，均相當吻合，能提供可靠的結果及參考依據。再針對不同噴嘴外型(N00、N05、N10、N15、N20)，分析轉接段對噴嘴性能及出口流場的影響。
噴嘴內的流場顯示隨著折流板角度改變，噴嘴內音速線（Sonic line）位置的移動、斜震波（Oblique shock）與膨脹扇（Expansion fan）也跟著改變。在固定壓力比下，出口的壓力分佈對總推力的貢獻不大，但向量角度到達20°的情形下，將產生推力的負壓損耗。
而加轉接段D1與無限長之轉接段假設(使得進入噴嘴流場為均勻流)的比較結果顯示，流經轉接段後，流場會因轉接段截面外型變化所導致的壓力梯度，產生壓力與速度的不均勻分佈，此流場變化對噴嘴的性能、推力角度無影響，但會改變其出口截面的壓力線分佈，尤其當噴嘴折流板偏折角改變小於10度時，其出口壓力扭曲值為入口均勻流的結果的兩倍。
減短轉接段的變化長度使轉接段內產生分離區，D2N00的結果中，非黏性解並無模擬出紊流解中出現的小區域分離，而D3N00於轉接段內出現大區域的分離，非黏性解之壁上壓力與壁上分離點位置與實驗值吻合。轉接段內分離區的出現對性能的影響並不顯著，但會因渦流的產生而導致轉接段內的冷卻問題。

In this study, numerical simulation is used to investigate the flow properties and nozzle performance of thrust-vectoring nozzles with high-aspect-ratio circular-to-rectangular transition duct. Using a third-order modified Osher-Chakravarthy (MOC) upwind finite volume method for space descritization and a explicit three-stage second order Runge-Kutta method for time descritization, the three-dimensional compressible Euler equations are solved. The configurations of investigated nozzles or transition ducts includes N00 (0°)、N05 (5°)、N10 (10°)、N15 (15°) 、N20 (20°) and D1 (Ld = 1.0)、D2 (Ld = 0.75)、D3 (Ld = 0.50) respectively.
With the present result of D1N00, we find that the inviscid-flow result is very close to that of experimental data. Namely, the viscous effect has less influence on the performance of thrust-vectoring system. Thus, we use inviscid-flow model to investigate the 3D thrust-vectoring system with ideal gas. The grid effect on the numerical solution is investigated.
For different flap angles, it is found that the sonic line, oblique shock and expansion fan are varied. With a fixed NPR value, pressure distribution at the nozzle exit has less contribution to net thrust. But when flap change angle reaches 20°, negative pressure difference at the nozzle exit results in the loss of net thrust.
From the results of cases D1N00~D1N20, the transition duct results in a non-uniform flow in the vectoring-thrust system. The non-uniform effect changes the pressure distribution at the nozzle exit. Especially when the average flap change angle is less than 10°, the pressure distortion is nearly twice of the result of the uniform inflow. Comparing the result of the D1 case with that of no transition duct(under uniform-inflow assumption), it is surprisingly found that the effect of the transition duct acting on the flow field has less influence to the performance of nozzle and thrust angles.
With shorter lengths of transition ducts (the D2、D3 cases), flow separation appears and results in a cooling problem of transition duct because of the vortex formation. Inviscid flow model doesn’t well predict small separation region in the D2N00 case, but predicts accurate wall pressure and separation point in the D3N00 case. In this case, there is a large separation region in the transition duct.

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