Interfacial shear in adiabatic downward gas/liquid co-current annular flow in pipes
Introduction
A large number of studies have been carried out on vertical air–water two-phase annular flow in pipes. This is not surprising considering the huge importance annular two-phase flow plays in the nuclear, chemical and petroleum industries where it is generally agreed to be one of the most frequently encountered flow patterns. To this end, many studies have been commissioned to investigate annular two-phase flow phenomena with the bulk of published works focussing on co-current upward annular flow. In sharp contrast there have been far fewer studies published on co-current downward annular two-phase flows. This is against the backdrop that co-current downward annular two-phase flow is also often encountered in engineering equipment such as gas absorbers as falling film flow, gas condensate pipelines, refrigeration systems, and in heat transfer equipment like boilers and heat exchangers. What little work is available is dominated by pipes of which the scales are much less than 100 mm in internal diameter. It has been noted that there is no guarantee that the use of models developed for these small pipes will predict large diameter flows well; therefore several reported studies [36], [31], [37], [38], [30], [39], [34], [40] have addressed that there is need to expand the knowledge of multiphase flow behaviour to large diameter pipe systems. For example, Oliemans et al. [36] compared entrainment correlations with large diameter test data and concluded there is not much confidence in the predictive value of the correlations. Kataoka and Ishii [31] showed that the application of the conventional drift flux model for pool void fraction prediction to relatively large vessels was only limited to low gas fluxes, and thus had to develop a new correlation for such large systems when annular flow for instance occurs at higher gas fluxes. Disturbance waves which greatly contribute to wall shear stress and are a source of entrained droplets were observed by Azzopardi et al. [8] to be incoherent in large diameter pipes. Careful observations revealed that in large pipes, the waves were not perpendicular to the flow direction but were curved “bow waves”. This is in sharp contrast to what is obtained in smaller tubes where the waves are continuous around the tube circumference. The study by Omebere-Iyari and Azzopardi [38] on disturbance wave velocity provided yet strong quantitative indication of pipe diameter effect on the gas–liquid interface behaviour. They established that Pearce’s coefficient, which is proportional to wave velocity, increases with pipe diameter such that its value of 0.9 remains fairly constant at large pipe diameters.
The interfacial friction factor has been likened to surface roughness in single-phase fluid flow [9], [43], [28]. In addition to the wall or skin friction in two-phase flow, interfacial friction as a result of slip between the two phases contributes to the frictional pressure loss. Therefore, the contribution of interfacial friction to the two-phase frictional component increases with increasing slip velocity or as the flow pattern moves from bubbly to annular flow. Klausner et al. [32] pointed out that the correlations of Henstock and Hanratty [27], Andreussi and Zanelli [5], and Asali et al. [7] are the only reported works that proposed relations for determining the downwards interfacial friction factor. Since then, Hajiloo et al. [26] and Dalkilic et al. [20] have developed downflow two-phase friction factor correlations, of which the former correlated data obtained from four different tube diameters ranging from 15.6 to 41.2 mm. The latter used data obtained for refrigerant HFC-134a in an 8.1 mm diameter vertical tube-in-tube heat exchanger and correlated the two-phase friction factor with an equivalent Reynolds number obtained as a function of gas quality and fluid density ratios. The physical correlating parameters used by Hajiloo et al. [26] using the friction length parameter and gas Reynolds number are similar to that earlier used by Asali et al. [7]. This method will further be extended in the present work using data obtained from a 101.6 mm large internal diameter pipe and it is envisaged to improve interfacial friction factor predictions for co-current downward air–water annular flow in large vertical pipelines.
Section snippets
Previous studies on downward two-phase interfacial friction factor empirical modelling
A number of empirical friction factor correlations have been put forward by prior investigators. Literature is replete with such correlations proposed for upward gas–liquid flow; however, some recommendations have been made for downward gas–liquid flow systems. The fluid combination used in most cases is air and water. Early downward co-current two-phase friction factor correlations were obtained by Chien and Ibele [13] and Fedotkin et al. [22]. Hajiloo et al. [26] noted that the results of the
Description of flow loop
The two-phase Serpent flow loop in the Oil and Gas Engineering Laboratory of Cranfield University is a specially-built test facility used in the study of flow behaviour around upward and downward pipes joined by U-bends. A schematic of this test apparatus is shown in Fig. 1. It is divided into three main parts: the fluid (air and water) supply and metering area, the test area, and the separation section. The flow rig receives measured rates of water and air from the flow metering area to the
New empirical correlation
In light of the various shortcomings of the published correlations, it is imperative to attempt to correlate our data separately which are characterised by large entrainments due to roll wave regime type entrainment caused by large shear resulting from the huge velocity differences between the phases. These resemble the premises used by Asali [6], Asali et al. [7] to correlate their data which were improvements to the rough sand analogue used by Henstock and Hanratty [27]. As turbulent
Concluding remarks
Several investigators have published studies showing that in turbulent multiphase flow systems, using correlations obtained from small diameter pipe systems to predict the behaviour of larger pipelines leaves much to be desired. An important class of such correlations are those predicting friction losses for the determination of pressure drops. Unfortunately, published large diameter friction flow data is scarce for developing new correlations, particularly for downward two-phase flow. In this
Acknowledgements
Aliyu M. Aliyu would like to express sincere gratitude to the Nigerian Government for the scholarship funding his PhD through the Petroleum Technology Development Fund’s Overseas Scholarship Scheme (PTDF/E/OSS/PHD/AMA/622/12).
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