Two-Phase Flow Pressure Change Across Sudden Contraction and Expansion in Small Channels

The flow of two-phase mixtures across sudden expansions and contractions is relevant in many applications such as chemical reactors, power generation units, oil wells and petrochemical plants. As the two-phase mixture flows through the sudden area changes, the flow might form a separation region at the sharp corner and introduce an irreversible pressure loss. This loss occurs in practical pipeline connections and in the heat exchangers. The small and narrow channels are widely adopted in compact heat exchangers. Also, flow in small rectangular channels is an integral part of CPU cold plate using the liquid cooling with or without phase change. Predictions of these pressure drops had been made using correlations developed for the conventional tubes, extrapolations of these correlations to small diameter tube are questionable.

In this study, the authors first give a short overview on the single-phase flow across sudden contraction and expansion, followed by a thorough review of the relevant literature for two-phase flow across sudden contraction and expansion. The applicability of the existing model/correlations for sudden contraction and expansion is then examined with the available data from literature. Comparisons for the pressure change data with the predictions of existing model/correlations indicate that none of them can accurately predict the data.

For the two-phase contraction, it is found that the influence of surface tension and outlet tube size, or equivalently the Bond number plays a major role for the departure of various models/correlations. Among the models/correlations being examined, the homogeneous model shows a little better than the others. Hence by taking into account the influences of gas quality, Bond number, Weber number and area ratio into the homogeneous model, a modified homogeneous correlation is proposed that considerably improves the predictive ability over existing correlations with a mean deviation of 30% to the 503 data.

For the two-phase expansion, most of the correlations highly over predict the data with a mini test section which has a Bond number being less than 0.1 in which the effect of surface tension dominates. Also, some of the correlations significantly under predict the data for very large test sections. Among the models/correlations being examined, the homogeneous model shows a poor predictive ability than the others, but it is handy from the engineering aspect. Hence by taking account the influences of Bond number, Weber number, Froude number, liquid Reynolds number, gas quality and area ratio into the original homogeneous model, a modified homogeneous model is proposed that considerably improves the predictive ability over existing correlations with a mean deviation of 23% and a standard deviation of 29% to the 282 data with wider ranges for application.

Keywords: Two-phase flow, pressure change, sudden contraction and expansion.