A new form of equation for force determination based on Navier-Stokes equations

Abstract

This work is focused on calculating the force effects of an incompressible homogeneous liquid on a surface of a rigid or a flexible tube. An unsteady flow induced by differential pressure at the beginning and at the end of the tube is assumed. The pressure difference for the unsteady flow is determined experimentally. The mathematical model is based on modified Navier-Stokes equations. The unsteady term is modified in order to be able to use the Gauss-Ostrogradsky theorem to calculate the force. This method of solution will allow the calculation of the force by integration of the Navier-Stokes equations, which will help to refine and simplify the calculations. In the article, both methods of force calculation will be presented and compared both through the ANSYS FEA and CFD ANSYS Fluent solvers and by the integration of the Navier-Stokes equation. The calculation will not only respect the compliance of the tube but also its movement status.This work is focused on calculating the force effects of an incompressible homogeneous liquid on a surface of a rigid or a flexible tube. An unsteady flow induced by differential pressure at the beginning and at the end of the tube is assumed. The pressure difference for the unsteady flow is determined experimentally. The mathematical model is based on modified Navier-Stokes equations. The unsteady term is modified in order to be able to use the Gauss-Ostrogradsky theorem to calculate the force. This method of solution will allow the calculation of the force by integration of the Navier-Stokes equations, which will help to refine and simplify the calculations. In the article, both methods of force calculation will be presented and compared both through the ANSYS FEA and CFD ANSYS Fluent solvers and by the integration of the Navier-Stokes equation. The calculation will not only respect the compliance of the tube but also its movement status.