Advances in the Physics and Computation of Compressible Liquid Transients

Accurate modeling of compressible liquid transients requires robust modeling of compressibility effects in a liquid, such as density variations and acoustic velocities. Efficient and case-adaptive friction models are crucial for the simulation accuracy of liquid transients. The paper reviews different mathematical models and their numerical implementation for compressible liquid transient simulations. Different aspects of compressible liquid transient modeling and simulation are profoundly explored with the help of relevant literature. The major aspects reviewed are the high-pressure applications of liquids, compressible modeling of liquids, gas shock tube simulation and its extension to liquid shock cases, the importance of numerical techniques such as Riemann solvers in simulation, the need for the development of benchmark results in compressible liquid flows, the evolution of unsteady friction modeling and limitations of models, and scope for improvement of valve-induced surge modeling. Almost every application where liquid compressibility effects are significant is covered under this review. A range of liquid equations of state for different liquids are discussed, and the compressible modeling of liquid water is profoundly analyzed by evaluating the performance of different state equations for the fluid. The significance of the gas shock tube problem in the branch of compressible flows is discussed, and the ways in which it could be extended to compressible liquid shock cases are elaborated through the conceptual problem of the water shock tube. The numerical techniques, especially the Riemann solvers, and the evolution of their different variants are explained with the help of relevant literature. Different formulations for steady and unsteady friction that are generally employed in mathematical models are analyzed, and their limitations for complex transient cases are discussed. Recent advancements in the unsteady friction formulation, such as the variable damping technique, are discussed, and its application to surge modeling is demonstrated. The experimental and numerical studies on valve-induced surges, their mathematical modeling, and the flow characteristics at the upstream and downstream locations of the valve are discussed in detail with the help of published literature. This review can serve as a single sufficient source for understanding the different aspects of compressible liquid transient modeling and to know the state-of-the-art in each aspect. The review also suggests the major directions in which future study is required based on the existing models' limitations and gaps in the literature.