When pipelines are rapidly filled, dynamic and sometimes dramatic air–water interactions often occur. These air–water interactions, along with their associated pressure and temperature oscillations, are explored in this paper both experimentally and numerically. A computational fluid dynamics (CFD) approach based on a volume of fluid (VOF) formulation is used to simulate the flow field in three-dimensions (3D). Thermal conduction and convection in three different media (air, liquid water, and the pipe wall) are all considered in order to account for the key thermal processes potentially influencing an entrapped air pocket during rapid filling. The simulation accounts for the compressibility of water and the roughness of the pipe wall, considerations sometimes neglected in previous studies. Simulated pressures and air–water profiles are compared to measured data and to the dynamic images obtained through a high-speed camera. The relatively good agreement between the numerical and experimental results confirms that the proposed model can accurately simulate transient flow and also reasonably represents the associated physical processes. Significantly, the observed phenomena of white mist and of a hot pipe wall are explained through the physics represented in the 3D simulations. Indeed, the model shows that extremely intense air–water interactions appear sufficient to account for the observed efficient heat exchange and the dramatic rates of energy dissipation. Overall, the proposed model provides insight into the physical mechanisms of rapid filling and particularly those thermal effects associated with entrapped air.

To simulate transient cavitating pipe flow, the discrete gas cavity model (DGCM) is combined with first-order and second-order finite-volume method (FVM) Godunov-type schemes. The earlier discrete vapor cavity model (DVCM) and DGCM based on the method of characteristics (MOC) are known to produce unrealistic pressure spikes. The new FVM-DGCM extends the previously developed FVM-DVCM through the introduction of a very small amount of free gas at the middle of each computation cell. Importantly, a pressure adjustment procedure is proposed to establish the relation between the cavity and the halves of the reach. Predictions of FVM-DGCM are compared with those of FVM-DVCM and MOC-DGCM and with experimental data. Results show that the proposed model reproduces the experimental pressure histories considerably better than the other two models. In particular, it produces fewer spikes, but—as in the old models—the first pressure peak due to cavity collapse is predicted much better than the subsequent peaks. The second-order FVM-DGCM is found to be accurate and robust, even for Courant numbers significantly less than 1.

In this study, an explicit track continuity algorithm is proposed for multitarget tracking (MTT) based on the Gaussian mixture (GM) implementation of the probability hypothesis density (PHD) filter. Trajectory maintenance and multitarget state extraction in the GM-PHD filter have not been effectively integrated to date. To address this problem, we propose an improved GM-PHD filter. In this approach, the Gaussian components are classified and labeled, and multitarget state extraction is converted into multiple single-state extractions. This provides the identity label of the individual target and can shield against the negative effects of clutter in the prior density region on the estimates, thus realizing the integration of trajectory maintenance with state extraction in the GM-PHD filter. As no additional associated procedures are required, the overall real-time performance of the proposed filter is similar to or slightly lower than that of the basic GM-PHD filter. The results of numerical experiments demonstrate that the proposed approach can achieve explicit track continuity.