Analysis and Numerical Simulation of the Stability of Axisymmetric Jets

本研究主要藉由奧爾索姆費爾德(Orr-Sommerfeld)方程式之線性 穩態理論分析與Phoenics套裝軟體之數值模擬，探討軸對稱噴流之穩 定性。 首先，在理論分析方面，探討雷諾數、頻率與激盪強度對噴流穩 定性之影響。其次，在數值模擬方面，藉由激盪噴流附加同相位擾動 (phase-locked velocity fluctuation)的方法，來描述主模態的空間 演化。更進一步，延伸出雙模態共振的觀念，以模擬基態(fundamental) 與副諧波(subharmonic)之間的共振效應，並描述渦對(vortex pairing) 的組化(pairing)現象。同時，應用能量積分法探討軸對稱噴流之穩定 性對於相位差、頻率差、以及激盪強度之改變而產生的變化。 最後，出最強穩態與最強非穩態的最佳化控制方法，並描述噴流 的七大演化。This research takes Orr-Sommerfeld linear stability theory as theoretical analysis, and meanwhile uses Phoenics computer pakeage to layout numerical simulation. At first, in the theoretical analysis, expects the variation of the Reynolds number of frequency makes what effect to the stability of axisymmetric jets. Next, for the numerical simulation, super-imposes some phase-locked fluctuation upon the jets to examine the spatial evolution of the preferred mode. Moreover, springs up the concept of couple modes to describe the resonant mechanism between the fundamental and the subharmonic. At the same time, identifies the changing of the stability of the exisymmetric jets responding to the varying of the phase difference, frequency difference, and excitation level difference by energy integral method. Then, represents the phenomenon of the vortex pairing. Conclusively, finds out the optimal control schemes for the strongest stability and the most energitic instability. Also, figures out the seven main evolution steps of jets