Data assimilation for modeling cavitation bubble dynamics

The original or modified Rayleigh Plesset equation (RPE) is often used to analyze cavitation bubble dynamics. The prediction accuracy of these equations is governed by the initial values of the physical parameters. However, even for higher fidelity models, deviations from experimental measurements are observed due to the models' underlying assumptions. Here, we present a novel state-observer data assimilation technique designed to fuse time-resolved cavitation bubble diameter measurements with a governing model to yield enhanced spatiotemporal prediction of the cavitation bubble dynamics. This technique places an observer variable in the original or modified RPE and uses a proportional–integral–derivative (PID) control law on the difference between the predicted and measured cavitation bubble diameter. The data-assimilated modeling most accurately estimates the bubble diameter and far-field pressure as the deviation of bubble diameter and far-field pressure predictions from measurements decrease by up to 90% and 60%, respectively. Although the assimilated model is not a substitude for high fidelity models, this technique overcomes the inherent model assumptions, and make the model’s outputs more robust with respect to the physical parameters' initial values.