The interaction of the Wave Phase Conjugation (WPC) process with bubble cloud dynamics is investigated via numerical modeling in application to bubble size measurements. The WPC simulator by Modarreszadeh and Timofeev (Computers and Fluids 197, 104353) is used as a starting point. In the simulator, a modified version of the high-order Nodal Discontinuous Galerkin method is used for modeling of acoustic wave propagation in the active WPC conjugator and the surrounding linear or non-linear fluid in 2D/axisymmetric domains. The effects of bubble dynamics are incorporated with the help of induced volume fractions. The modified Keller-Miksis model is employed to simulate vibrations of bubbles subjected to acoustic waves. After thorough verification and validation of the numerical scheme and the physical model, the interaction of various bubble clouds, including poly-disperse ones, with the WPC process is examined with the help of some existing and newly suggested descriptive indicators, e.g., the amplification factor and the absolute and relative signal intensities. The results show that signals scattered from bubble-plane clouds, in which the bubbles are non-physically synced, are strong enough to affect the modulation process if the stimulation frequency is close to the natural frequency of bubbles. For more realistic bubble clouds, the modulation process is almost intact. However, conjugate waves do carry some signatures of bubble-cloud dynamics, e.g., signals with frequencies higher than the natural frequency of bubbles are significantly diminished. The study demonstrates that WPC-based techniques have a promising potential to be used for measuring bubble dimensions.

波数值共轭（WPC）过程与气泡云动力学之间的相互作用是通过数值模型应用于气泡尺寸测量研究的。Modarreszadeh和Timofeev的WPC模拟器（计算机和流体197，104353）被用作起点。在模拟器中，使用高阶节点间断Galerkin方法的改进版本对有源WPC共轭器和2D /轴对称域中周围的线性或非线性流体中的声波传播进行建模。气泡动力学的影响在诱导的体积分数的帮助下被并入。修改后的Keller-Miksis模型用于模拟气泡在声波作用下的振动。在对数值方案和物理模型进行了彻底的验证和确认之后，各种气泡云之间的相互作用，包括多分散的WPC过程在内的WPC过程，借助于一些现有的和新建议的描述性指标进行了检验，例如，放大系数以及绝对信号强度和相对信号强度。结果表明，如果刺激频率接近气泡的固有频率，则气泡从气泡平面云散发出的信号强度很强，足以影响调制过程，其中气泡是非物理同步的。对于更逼真的气泡云，调制过程几乎是完整的。但是，共轭波确实带有气泡云动力学的某些特征，例如，频率高于气泡自然频率的信号会大大降低。这项研究表明，基于WPC的技术在测量气泡尺寸方面具有广阔的前景。