## 1 Introduction  
Water pipelines are hydraulic infrastructures that supply and distribute water from the point of origin to the points of water demand. The water supply systems are divided into the following infrastructures: (i) raw water pipelines, (ii) drinking water pipelines, and (iii) water distribution networks [1]. Pipeline filling and emptying processes in pressurised systems are critical operations in hydraulic engineering [2], as they involve transient two-phase air-water interactions that can lead to severe pressure surges, vacuum conditions, and potential structural damage [3; 4; 5; 6]. Accurately predicting and controlling these transient phenomena are essential to ensuring operational safety and efficiency. In that sense, Digital Twin (DT) technologies have emerged as powerful tools for modelling and optimising water flow efficiency [7; 8; 9]. DTs for water distribution systems can harness static and dynamic big data collection and management, including SCADA and IoT data, to represent system performance more accurately, generate valuable insights, and support actionable outcomes for managers, operators, and users [10; 11]. DTs facilitate the integration of artificial intelligence (AI), enhancing decision-making processes. System managers increasingly utilise DTs to optimise all system management [12; 13; 14]. In control and emergency centres, hydraulic simulators powered by DTs allow operators to simulate responses to emergencies such as pipeline failures, rupture occurrences, leakage increases, fraud water connections, and water supply outages [15]. Implementing these advanced interactive tools enhances system-wide awareness and supports the sustainability and efficiency of water pipe systems by integrating real-time measurement data [16; 17; 18]. DTs for water distribution systems have been applied using one-dimensional mathematical model approaches for single-phase (water) flows, and they have been integrated with real-time monitoring to represent typical scenarios that can be useful for making decisions. For example, [PERSON] et al. [19] developed a DT based on a one-dimensional mathematical model that was applied to water distribution networks, integrating sensors and real-time data analysis to supply datasets concerning hydraulic parameters for making decisions, where its key contribution was the significant reduction in water losses. [PERSON] et al. [20] implemented a DT to manage a drinking water distribution network in Valencia, Spain. Their main contribution was developing the GO2 HydNet system based on mathematical models, an application that integrated hydraulic models with real-time data from GIS, SCADA, and IoT sensors. This allowed for the accurate simulation of network behaviour in past, present, and future scenarios, facilitating decision-making for planning, operation, and emergency response. [PERSON] et al. [16] implemented a DT for the sustainable management of pressurised water systems based on hydraulic modelling (EPANET) with sustainability indicators (social, economic, and environmental). The model optimised water and energy efficiency, achieving reductions in energy consumption, as well as generating 103,710 kWh/year of renewable energy. Although DTs based on one-dimensional models can effectively predict specific hydraulic parameters in both steady and unsteady flow conditions, they treat the flow as a single-phase (water) flow, which limits their ability to capture the effects of air-water interaction. In need of more information on two-phase transient flows in pressurised pipelines, Computational Fluid Dynamics (CFD) models have been developed in some research to understand the hydraulic and thermodynamic phenomena in water infrastructure [21]. Unlike one-dimensional models, CFD models allow for detailed spatial resolution and provide valuable information in both the temporal and spatial domains using contours [22; 23], allowing the study of local-scale phenomena such as the shape and movement of air bubbles [6; 24].