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拋物面反射體上震波聚焦引起渦流現象之實驗及數值研究
Experimental and Numerical Studies on Vortical Flows Induced by Shock Wave Focusing over Parabolic Reflectors
摘要
本文同時應用數值計算模擬及實驗量測觀測的方法，探討以空氣爲介質的平面震波，入射到二維的拋物面反射體反射後，造成震波聚焦所引起渦流的現象，研究流場的機制及渦流發生的原因。對於流場的實驗觀測採用color schlieren的光學技術拍攝流場的影像，並以壓力感測器量測聚焦區對稱軸上的壓力變化。數值模擬的方法採用Yee及Harten所發展並經Liang等人所改良的upwind TVD數值法，應用有限體積法，考慮真實氣體效應，並以Newton次疊代法提高時間的準確性，解非穩態的震波聚焦流場。本文中觀察弱入射震波馬赫數爲1.2，及強入射震波馬赫數爲1.85，在兩個不同凹面深度的反射體上反射後的過程。本研究中發現，震波聚焦之後將發兩組渦流，第一組渦流發生在靠近反射體表面，爲additional shock與滑流線交互作用所引起。第二組渦流發生在聚焦點附近，其發生的原因爲反射震波與滑流線交互作用引起的。
並列摘要
The problem of a plane shock wave propagating in an air media over a two-dimensional parabolic reflector is investigated. The shock wave after reflecting from the parabolic concave reflector forms a converging concave shock wave. The converging concave reflected shock wave will focus and result in a complicated flow field with vortices. For studying this problem, both experimental and computational approaches are employed. The experimental approach is to use a color schlieren optical photography for recording the images of the flow field causing by shock wave focusing on color films. Moreover, two sets of piezo-electric pressure transducers are arranged to measure the incident shock speed and the dynamic pressures in the focal region. The computational approach is to simulate the flow field caused by shock wave focusing by solving the compressible Navier-Stokes equations To solve the equations, an implicit TVD scheme with an improved flux limiter and an inner iteration for enhancing stability and accuracy. The real-gas effect i• taken into account through a proper correction of the specific heat ratio of air, when high temperature occurs due to shock wave focusing. Two values of incident shock Mach number (Ms) and two parabolic reflectors with different focal lengths are chosen. Ms=1.2 corresponds to a weaker shock, and Ms 1.85 for a stronger shock. It was found that shock wave focusing generates two vortical flow regions. One is near the reflector surface. In this region the vortical flow is resulted from the interaction between an additional shock and the slip line. The other is. near the focal region. For the latter case, the vortical flow is resulted from the interaction of the reflected shock and the slip line.