Some investigations on the mean and fluctuating velocities of an oscillating Taylor bubble

The slug flow characterized by large elongated bubbles also called Taylor bubbles is widely encountered in nuclear reactor steam generators, cooling plants, reboilers, etc. The analysis of slug flow is very important as the instability caused by such flows can affect the safety features of nuclear reactors and other two-phase flow equipments. In this paper, we study the motion of a Taylor bubble rising in stagnant fluids in a vertical oscillating pipe. The investigation is restricted to high Reynolds numbers and to an intermediate range of Bond numbers where the effects of surface tension can be considered. The Froude number ranged between 0.22 and 0.33. Firstly, detailed analysis of models proposed in the literature for the motion of a Taylor bubble in an unsteady acceleration field is realized. The velocity differential equation obtained in the case of potential and axisymmetric flow without surface tension given in the literature is first non-dimensionalized to highlight dimensionless numbers. Then, the instantaneous velocity of the bubble is numerically determined. Mean and fluctuating velocities as well as the phase shift ( U ¯ b , Uf and ϕ) are estimated by using a technique based on the nonlinear least squares method. Results enable a discussion on the role played by dimensionless numbers on the dynamics of the bubble. It is found that the two parameters, the relative acceleration and the Bond number (a and Bo) have a governing role on the evolution of mean and fluctuating velocities while the ratio of the oscillation amplitude to the pipe diameter (b/D) has little influence when b/D > 10−1. Further, the velocities U ¯ b and Uf as well as the phase shift ϕ are experimentally investigated. Correlations allowing the prediction of mean and fluctuating velocities as well as the phase shift depending on the Bond number and relative acceleration are proposed. The correlations are found to be in good agreement with our experimental results obtained in a previous work.