Numerical investigation of hydraulic jump in pipelines at two-phase flow

1. Introduction
One of the phenomena that has been studied both theoretically and experimentally in hydraulic engineering is hydraulic jump. Hydraulic jump causes the flow to lose a considerable amount of energy due to the change in its regime from supercritical to subcritical. Since fluid flows in a conduit may be either of a free type (open-channels hydraulic) or of an under-pressure type (under pressure conduits hydraulic), the hydraulic jump can occur in both situations regarding the type and function of the system. Therefore, it can be said that hydraulic jump can occur in open channels as stilling basin. It can also occur in downward inclined pipes that contain a large air package. Additionally, since the present paper deals with pipelines, the following general statements can be mentioned about them. Pipelines are used to transfer fluids such as water, oil, gas, and wastewater offshore or onshore, either in the form of two-phase or multi-phase flows. The importance and function of the flows inside the pipeline must be studied. Export pipelines transfer fluids from platforms or FPSO (Floating Production, Storage, and Offloading) to the beach and they usually contain gas-condensate or oil with a little water. Infield pipelines transfer flows from the wells or manifolds to the platform or FPSO [Guo et al (2014)]. Offshore pipeline design includes structural, geometrical, and hydraulic designs. In structural design such matters as buckling and collapse during pipeline operation are considered, and several studies have been carried out regarding these matters. In geometrical design, diameter determination parameters (based on the flow capacity and precise analysis of the flow assurance in offshore pipelines), and wall thickness (according to the standards) are considered, each of which is somehow related to the flow hydraulics. Therefore, hydraulic design of pipeline is of utmost importance and problems related to this area must be examined precisely. However, it needs to be considered that most of the studies about hydraulic jump are carried out on channels, open conduits and stilling basin. Flows in open channels can shift from supercritical to subcritical. Such shifts happen very suddenly and appear due to hydraulic jump [Akan (2006), Lauchlan (2005) and Vasconcelos and Wright, (2009)]. Most of the studies about the hydraulic of pipelines that contain multi-phase liquid and gas flows concentrate on the function of flow regimes, pressure and sever slug. Therefore, it can be claimed that there is a lack in studying hydraulic jump in under pressure pipelines with multi-phase liquid-gas flows, because most of the studies are carried out on wastewater transfer lines and open conduits. The present paper, therefore, deals with the numerical analysis of hydraulic jump in pipelines with two phase water-air flows. To this aim, some experimental information has been taken from Pothof (2011) to verify the accuracy of findings and numerical modeling. It must be noted that Pothof has worked on wastewater pipelines that function gravitationally, while this study deals with under pressure pipelines in offshore conditions.
2. Methodology
Regarding Pothof's experimental work (2011) which analyzes the occurrence of hydraulic jump, and using its data, the hydraulic jump is then numerically analyzed.
In order to analyze the hydraulic jump numerically, roughness values, geometrical properties of the pipeline, and the angles are specified. General characteristics of the submerged pipe are also presented. Some other properties include: diameter=8in, water flowrate=128160kg/hr, air flowrate=32040kg/hr.
Pressure loss in pipelines with multi-phase flows, includes frictional and hydrostatic pressure loss, is calculated based on mixture density and velocity. In hydrostatic pressure loss, it must be noted that since in horizontal pipelines ΔZ=0, the pressure loss is therefore zero, too. In upward inclined pipelines this value is positive (in line with increasing the total loss) and in downward inclined pipelines it is negative (in line with decreasing the total loss).
In order to determine flow regimes semi-theoretically, Taitel and Dukler (1976) first modeled a stratified flow in a pipe, presupposing that the flow has been stable. Then, they determined how the flow regime was transferred from stratified to other flow regimes. The results of their analyses that are presented in a map for two-phase gas-liquid flow is used in this paper to determine flow regimes in two phase flow.
3. Discussion
Hydraulic jump occurs in open water transfer structures and channels and its behavior and occurrence in such situations is studied precisely. Similarly, it is important to study it in pipelines, because it affects the behavior of the fluid inside the pipeline. When there is a pipeline containing a two-phase water-air flow, it can be assumed that the fluid inside the pipeline might face a hydraulic jump. Predicting such a phenomenon and its effects on pipeline during its working lifetime is a very important issue in the industries that deal with pipelines which transfer multi-phase fluids. Therefore, the present paper studies the occurrence of hydraulic jump in pipelines with two-phase water-air flows.
4. Conclusion
It can be concluded, based on the hydraulic gradient and the resulted losses, that hydraulic jump occurs when there is some air in the pipeline; and as the experimental researches showed, as the angle increases, the jump height increases, too. In all of the above- mentioned analyses except for the mode in which the angle is 30 degrees, flow regimes, according to Taitel and Dukler are annular mist for A-B, annular mist for B-C, and annular mist for B-D. Regarding what has been said, it can be stated that when total pressure loss in the negative direction (i.e., when the hydrostatic loss overcomes frictional loss) approaches zero, the flow regime might change.
5. Keywords: Flow pattern, multi-phase flow, hydraulic jump, flow regime, Taitel and Dukler