Abstract We analyse the controlled generation of bubbles of a given size at a determined bubbling rate in a co-flowing water stream forcing the gas flow. The temporal evolution of the bubble size, R(t), the air flow rate, Qa(t), and the pressure evolution inside the bubble, pb(t), during the bubbling process are reported. To that aim, the temporal evolution of the bubble shape and the pressure inside the air feeding chamber, pc(t), where a harmonic perturbation is induced using a loudspeaker, are obtained from high-speed images synchronized with pressure measurements. A model is developed to describe the unsteady motion of the gas stream along the injection needle, coupled with the Rayleigh-Plesset equation for the growing bubble, allowing us to obtain pb(t). Thus, the minimum pressure amplitudes required inside the forming bubble to control their size and bubbling frequency are provided as a function of the gas flow rate, the liquid velocity, uw, and the forcing frequency, ff. Two different behaviors have been observed, depending on the liquid-to-gas velocity ratio, Λ = u w / u a . For small enough values of Λ, the critical pressure amplitude is given by p s ∼ ρ a c u a S t f 3 , associated to a rapid pressure increase taking place during an interval of time of the order of the acoustic time. However, for larger values of Λ, p s ∼ ρ u w 2 S t f 3 Λ − 1 / 5 W e − 1 / 4 . Here ρ and ρa are the liquid and gas densities respectively, c the speed of sound in air and S t f = f f r o / u w and W e = ρ u w 2 r o / σ the Strouhal and Weber numbers, where ro denotes the outer radius of the injector.

中文翻译：

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在强制同轴空气-水射流中控制鼓泡过程的鼓泡压力要求。

摘要 我们分析了在共同流动的水流中以确定的起泡速率控制产生给定尺寸的气泡，从而迫使气体流动。报告了鼓泡过程中气泡大小 R(t)、空气流速 Qa(t) 和气泡内部压力演变 pb(t) 的时间演变。为此，从与压力测量同步的高速图像中获得气泡形状的时间演变和空气供给室内的压力 pc(t)，其中使用扬声器引起谐波扰动。开发了一个模型来描述气流沿注射针的非定常运动，再加上气泡增长的 Rayleigh-Plesset 方程，使我们能够获得 pb(t)。因此，形成气泡内部控制它们的大小和起泡频率所需的最小压力幅度作为气体流速、液体速度 uw 和强迫频率 ff 的函数提供。已经观察到两种不同的行为，这取决于液气速度比 Λ = uw / ua 。对于足够小的 Λ 值，临界压力振幅由 ps ∼ ρ acua S tf 3 给出，这与在声学时间数量级的时间间隔期间发生的快速压力增加有关。然而，对于较大的 Λ 值，ps ∼ ρ uw 2 S tf 3 Λ − 1 / 5 We − 1 / 4 。这里 ρ 和 ρa 分别是液体和气体的密度，c 是空气中的声速，S tf = ffro / uw 和 We = ρ uw 2 ro / σ 斯特劳哈尔数和韦伯数，其中 ro 表示外半径注射器。