Numerical simulation of various flow regimes in water delivery systems

Abstract

Transient flow frequently occurs in water delivery systems, including various flow regimes such as water hammer, free surface flow, and slug flow. Current models often oversimplify these phenomena by simulating single-phase flow or using simplistic one-dimensional assumptions for the gas-water interface, neglecting interface instability. Although two-fluid models can address some of these issues, they cannot simulate open channel flow and have not yet been applied to transient flow scenarios. To date, no single model has been able to simultaneously simulate all these flow regimes while overcoming these limitations. To address this gap, the two-fluid model is enhanced in this paper. For water hammer simulation, a gas volume fraction of zero is assumed, and a TVB unsteady friction model is introduced to enhance numerical accuracy. For open channel flow, a variable wave speed equation and a new state equation are presented. Despite the different state equations required for various flow regimes, a Roe-type scheme is introduced to solve the two-fluid model. This approach accurately simulates water hammer, free surface flow (including open channel flow and stratified flow), and slug flow. An experimental pipeline system is designed to validate the proposed model's ability to simulate water hammer. Additionally, several cases are used to verify the model's capability in simulating open channel flow, stratified flow, and slug flow. The model accurately predicts the occurrence of slug flow, consistent with experimental flow pattern maps, and effectively simulates the evolution of slug flow, closely matching the measured gas-water interface. The effects of gas volume fraction, pipe length, and pipe slope on slug flow are systematically discussed. Results indicate that smaller initial gas volume fractions, longer pipe lengths, and upward pipe slopes increase the likelihood of slug flow generation within the pipeline, which should be minimized during design.Abbreviations: TVB: Trikha-Vardy-Brown model; Cr: Courant number

Keywords

• Transient flow
• gas-water interface
• slug flow
• two-fluid model