Air-water two-phase bubbly flow across 90° vertical elbows Part II: Modeling

Following Part (I) of the current study, which presents the experimental results of the elbow effects on two-phase flow parameters in bubbly flow, Part (II) develops models and correlations to predict the evolution of these parameters across and downstream of 90° vertical-upward and vertical-downward elbows. To quantify the length requires for the effects of the elbows to dissipate (or the dissipation length), the strength of elbows is defined as the variance of the local void fraction distribution. The axial development of the elbow-strength is modeled by an exponential function of the axial development length based on the experimental data. Then, the dissipation length of the elbow is determined by characterizing the evolution of the elbow-strength parameter. The elbow-strength parameter is also used to correlate the void-weighted bubble velocity and covariance terms in the interfacial area transport equation (IATE). The two-phase pressure drop across vertical elbows is modeled with a modified Lockhart-Martinelli correlation which considers the additional pressure drop induced by elbows. To evaluate the above developed models and correlations, they are implemented into the IATE applicable to the elbow-influenced region. The established IATE together with the available IATE of different flow orientations in straight channels are implemented to predict the interfacial area transport from the vertical-upward to horizontal to vertical-downward two-phase flow across elbows. It is found that the interfacial area concentration predictions are in good agreement with the experimental data with an average absolute percent difference of ±6% throughout the test section. The individual contributions to the interfacial area concentration transport due to each source and sink term in the IATE are discussed, demonstrating that the models and correlations developed for the two-phase flow parameters in elbow regions are reliable.