Reconstruction of gas–liquid flows using the stochastic estimation with a 16-channel electrode array

Bubble-injection methods are considered to be a prospective approach to reduce skin-frictional drag for ships. To apply this technique for unsteady flows, we attempt to introduce a feedback loop of air injection in future applications. Hence, we wish to establish reduced-order models of unsteady bubbly flows from the information at the bottom of the ship, but this must be achieved with a limited number of sensors in practice. This motivates us to develop a reconstruction technique that recovers instantaneous phase information of gas–liquid flows. This study introduces the so-called stochastic estimation and reconstructs bubble distribution based on electrical impedance. We simulate the flow at the bottom of a ship using a horizontal channel and install a 16-channel electrode array on the upper wall to acquire time histories of electrical impedance. The relation between the bubble distribution and the electrical impedance is determined by simultaneous image measurement using a high-speed video camera. Once the coefficients of the linear relation between the electrical impedance and the local void fraction are calculated, two-dimensional bubble distribution can be estimated from only voltages at the 16 electrodes. The proposed technique is examined over a range of void fractions and flow velocities, and the capabilities of the stochastic estimation applied to bubbly flow reconstruction are demonstrated by comparing the reconstructed/predicted images with the original ones