球對稱氣泡內聲光效應之研究

Abstract

聲光效應是一種利用聲波使液體中的氣泡發光的現象，本論文以數值方法探討不同氣泡初始半徑 、不同聲波頻率 、不同聲波振幅 個別對聲光效應的影響。聲光效應中，氣泡半徑的運動方程式可以由Rayleigh-Plesset方程式來描述，氣泡內的流場在運動過程則假設了”均勻分布模型”與”凡得瓦狀態模型”，論文中以二階Runge-Kutta method求解”均勻分布模型”，以Lax-Friedrich scheme求解shock-wave model的”凡得瓦狀態模型”。由”均勻分布模型”的結果可看出 越小、 越小、 越大則越容易觀察到聲光效應的現象；而凡得瓦狀態模型的離散方法由於有嚴重的數值耗散，得到的結果相當接近”均勻分布模型”，而不如預期中，應該觀察到震波的產生，未來可在離散中加入”震波捕獲法”以改善”凡得瓦狀態模型”的結果。 在2002年，Taleyarkhan等人[27]提出聲光效應的氣泡內，有發生”核融合反應”的可能性，在地球能源日漸短缺的這個年代，或許聲光效應也可以在能源的領域拓展出一片新天地。

Sonoluminescence is a light emission phenomenon from collapsing bubbles in liquid stimulated by an ultrasonic wave. In this study, the influences of the bubble ambient radius , the frequency of acoustic wave , and the amplitude of acoustic wave on the sonoluminescence are investigated numerically. The radius of a gas-filled bubble in a liquid is governed by the Rayleigh-Plesset equation. The behavior of the gas within the bubble is modeled by two different models - ”uniform adiabatic model” and “adiabatic van der Waals model”. The uniform adiabatic model is solved by a 2nd-order Runge-Kutta method and the adiabatic van der Waals model is solved by the Lax-Friedrich scheme. From the results of the uniform adiabatic model, we conclude that the smaller , and the smaller , and the larger , the easier the sonoluminescence is observed. However, because there is terrible numerical dissipation due to the discretization, the results of the adiabatic van der Waals model are nothing different from the uniform adiabatic model. To improve the accuracy of the adiabatic van der Waals model, a proper shock-capturing scheme must be implemented in the future. In 2002, Taleyarkhan et al.[27] reported the possibility of the “Bubble Fusion”. Maybe sonoluminescence can be another way to develop new energy.