behnam cheraghi

The present paper introduces the implementation of a concurrent solver for pressure and velocity to solve free surface flows within the foam-extend framework. Integrating pressure and velocity fields with interface tracking algorithm has led to the development of a solver equivalent to the base foam-extend solver, named interTrackFoam. The current algorithm is entirely implemented using the structures, classes, and functions available in the foam-extend framework, and all the capabilities of this framework remain usable. Additionally, this solver utilizes libraries related to block matrices in foam-extend along with parallel solving capabilities. The block matrix system serves as the foundation for the concurrent solver. Notably, reducing the number of inner loops and performing one-step pressure and velocity solving are among the primary differences from the recognized default solver. Essentially, this solver represents the initial step towards a concurrent solver for velocity, pressure, temperature, and constituents with heat and mass transfer capabilities. The solver's capability is demonstrated through solving various experimental cases, including three-dimensional reservoirs, free surface flow around airfoils, and flow over sloping surfaces. With the concurrent solving capability of pressure and velocity, this solver holds significant potential in addressing complex physics and geometries. The ability for simultaneous solving enables reducing iterations or considering relatively higher time steps for flow computation.

Free hydroelastic coupled vibration analysis of frictionless liquids with a free surface in spherical tanks with a flexible bottom has been performed. The side wall has been considered to treate as a rigid body. The flexible bottom treats as a membrane at a certain distance bellow the center point, and the free surface is considered as a cross cutting at the top of the center point. The spherical coordinate system is adopted to derive the governing coupled equations, and finally a vibration analysis is carried out, using the traditional Galerkin's method, leading to closed-form solutions. Effects of various system parameters, i.e., membrane tension, liquid density, geometric parameters of the system such as the container radius, free surface distance discriminate parameter, and bottom distance discriminate parameter on the vibration behavior are investigated. The novelty of the present work is to obtain direct formulas for hydroelastic coupled vibration analysis of the mentioned system, which can be easily used in engineering design applications. Coupling between two mode numbers can be clearly seen in results, in other words, there is a coupling between vibration modes as interaction in spherical geometry.