Dynamic Force on an Elbow Caused by a Traveling Liquid Slug

Abstract

The impact force on an elbow induced by traveling isolated liquid slugs in a horizontal pipeline is studied. A literature review reveals that the force on the elbow is mainly due to momentum transfer in changing the fluid flow direction around the elbow. Therefore, to accurately calculate the magnitude and duration of the impact force, the slug arrival velocity at the elbow needs to be well predicted. The hydrodynamic behavior of the slug passing through the elbow needs to be properly modeled too. A combination of 1D and 2D models is used in this paper to analyze this problem. The 1D model is used to predict the slug motion in the horizontal pipeline. With the obtained slug arrival velocity, slug length, and driving air pressure as initial conditions, the 2D Euler equations are solved by the smoothed particle hydrodynamics (SPH) method to analyze the slug dynamics at the elbow. The 2D SPH solution matches experimental data and clearly demonstrates the occurrence of flow separation at the elbow, which is a typical effect of high Reynolds flows. Using the obtained flow contraction coefficient, an improved 1D model with nonlinear elbow resistance is proposed and solved by SPH. The 1D SPH results show the best fit with experimental data obtained so far.

An Improved 1D Model for Liquid Slugs Travelling in Pipelines

“…This formula is different from the one given in [1], where the slightly larger distance travelled by the slug tail was considered. …”

“…Equations (9a) and (9b) can be combined into one strongly nonlinear second-order ODE for L, but there is no obvious advantage when solving the system numerically. Equation (9a) is an improvement with respect to previous work by the authors [1,2], in the sense that the factors containing  are more accurate now. The first term on the right in Eq.…”

“…It is used to predict the velocity and length of the slug at the instant it arrives at an obstacle, such as an elbow. In [1] it was demonstrated that flow separation occurs at the elbow (Fig. 3), and that this can be modelled by switching on an additional "resistance" in Eq.…”

“…[1]. An alternative derivation (using Leibniz's rule) and refinement of the 1D model used in [1,2] is presented in the Appendix herein.…”

“…[1]. An alternative derivation (using Leibniz's rule) and refinement of the 1D model used in [1,2] is presented in the Appendix herein. The refinement is that in the equation of motion the slug velocity is not taken uniform, but linearly increasing from front to tail.…”