Understanding and modelling of transient air-water flows in urban stormwater drainage system : with a focus on spring-like geyser

Abstract

Extreme rainstorm events and the associated urban flooding disasters have become more and more frequent and intensive in the world, which have caused enormous losses in social and economic resources. Previous studies and field observations have evidenced that such urban flooding accidents could be caused and exacerbated by the system drainage capacity reduction due to the occurrence of transient air-water flows within the systems under sudden and fast drainage conditions. Therefore, a comprehensive understanding and analysis of the transient interaction and evolution process between the air and water flows/phases is of significance and necessity, which is however not very clear about its physical formulation and development mechanism for current theory and practice. Motivated by this objective, the present thesis research aims to understand the physical mechanism and model the evolution process of transient air-water flows under various initial and boundary conditions. Coded in a distributed framework based on the user-friendly MATLAB platform, the numerical model solving the full 2D Navier-Stokes equations with a coupled method of level set (LS) and volume of fluid (VOF) schemes is first developed in this research. This proposed model and numerical method could accurately capture the air-water interface evolution details through straightforward algorithms as well as fully represent physical conservation characteristics. With the well-established benchmark cases in the literature, the developed 2D model and numerical method are fully validated and verified to be of sufficiently accuracy, efficiency and stability to reproduce the complete different flow surface profiles and air-water interface dynamics during the highly unsteady flow process such as the bubble rising process, as well as the temporal and spatial evolutions of velocity and pressure distributions, which are crucial to in-depth understand the mechanism and process of such complex two-phase flows in practical engineering systems. Afterwards, the validated 2D model is applied to extensive application cases, with perspective for a detailed and systematic analysis of transient air-water flows under different conditions encountered in real-life stormwater drainage engineering systems. Specifically, the rapid filling process in stormwater drainage systems is investigated for understanding different influential parameters of the initial and boundary conditions on the dynamic air-water interface evolution. With the 2D modelling results and analysis, the underlying physics of rapid filling process is explored by the energy transformation relationship as well as the velocity and pressure distribution variation patterns of both air and water phases. To explain, the 1D analytical analysis based on different assumptions is performed and compared with the 2D model results, so as to further highlight and understand the key parameters which may dominate the transient air-water interactions. The comparison and analysis results indicate that the system with closed wall boundary is capable to conserve more energy and keep a constant propagating speed before the stagnant point reaches the upstream end, while the system with well-ventilated outlet may suffer more fierce water column collapsing within instant moment, so that more energy loss occurs and the accelerated waves to the downstream end could retain the relatively higher drainage capacity. Besides, the changes of the upstream drainage pressure and the drainage conduit slope conditions could greatly affect the transformation and patterns of different energy forms, and thus the dynamic air-water interactions during the rapid filling process. Based on the results and findings of rapid filling process, the complex transient air-water spring-like geysering (or inertia surcharging) problem with consisting of both horizontal pipe filling and vertical bubble rising processes are then investigated by the developed 2D model, so as to examine and explain the influence of different system parameters and flow conditions to the formation mechanism and propagation process of such spring-like geyser eruptions/surges in the stormwater drainage systems, which is one of the main objectives of this thesis research. The influence factors for inspection include the size ratio of the diameter of drainage pipe and vertical riser, initial pressure and velocity settings. Extensive numerical simulation cases are conducted for systematic analysis to ascertain the dominating factors affecting the variation magnitude and evolution process of pressure and velocity distributions as well as the transformation patterns of different energy forms. The application results demonstrate that the large-size air pocket tends to be more vulnerable and fragile to break into pieces during bubble rising process with more contact area with water, which is suffered greater probability for deformation of bubble shape and corresponding larger variation of pressure and velocity distributions. In addition, the motion of air phase (entrapped air bubbles/pockets) may have notable influence on the transformation of different energy forms during the distortions of air-water interfaces under different initial and boundary conditions, which thus plays a pivotal role to the whole formation and evolution processes of air-water mixture geysering/surcharging in the drainage system.