Unsteady Friction Modeling Technique for Lagrangian Approaches in Transient Simulations

Abstract

This study tackles the problem of simulating the head damping effect in transient flows when modeled in the Lagrangian approach rather than Eulerian. The Lagrangian approach normally requires orders of magnitude fewer calculations, which allows very large systems to be solved in an expeditious manner, and it has the additional advantage of using a simple physical model as the basis for its development. Moreover, since it is continuous in both time and space, the method is less sensitive to the structure of the network and the length of the simulation process, resulting in improved computational efficiency. Nevertheless, most recent studies used an Eulerian approach when simulating the systems transient response (e.g., method of characteristics), thus focused on developing and improving different computational routines for modeling and simulating unsteady friction models that are better fixated for Eulerian methods and are not suited for Lagrangian ones. One-dimensional methods of representing unsteady contributions to skin friction based on instantaneous acceleration have a long track record (e.g., Daily et al. 1956, Carstens and Roller 1959). And it is still the most popular method in software used for practical simulations, despite it cannot accurately depict the system's transient responses without additional calibrations and tunings. However, the more accurate models (e.g., Brunone 2000) are not suited for the Lagrangian approach. The lack of a mesh structure in the Lagrangian approach makes it challenging to consider the convective acceleration terms in addition to the local acceleration. Therefore, there is a need for a more accurate friction model that is suited for Lagrangian methods without compromising their performance. Unfortunately, such a model is yet to be published in the literature. This study presents a new friction modeling technique that compensates for both the local and convective acceleration terms for the Lagrangian transient modeling approach, without compromising the computational time. Additionally, fixating only on the Eulerian approach for transient modeling and undermining the Lagrangian based models is concerning since it can provide different perspectives for developing novel solutions and tools that take advantage of transient events.