publication . Other literature type . Preprint . Article . 2019

Geometric Theory of Flexible and Expandable Tubes Conveying Fluid: Equations, Solutions and Shock Waves

François Gay-Balmaz; Vakhtang Putkaradze;
  • Published: 01 Apr 2019
  • Publisher: Springer Science and Business Media LLC
Abstract
International audience; We present a theory for the three-dimensional evolution of tubes with expandable walls conveying fluid. Our theory can accommodate arbitrary deformations of the tube, arbitrary elasticity of the walls, and both compressible and incompressible flows inside the tube. We also present the theory of propagation of shock waves in such tubes and derive the conservation laws and Rankine-Hugoniot conditions in arbitrary spatial configuration of the tubes, and compute several examples of particular solutions. The theory is derived from a variational treatment of Cosserat rod theory extended to incorporate expandable walls and moving flow inside the...
Subjects
arXiv: Physics::Fluid Dynamics
free text keywords: Physics - Fluid Dynamics, Mathematics - Dynamical Systems, Nonlinear Sciences - Chaotic Dynamics, [MATH]Mathematics [math], [NLIN]Nonlinear Sciences [physics], General Engineering, Modelling and Simulation, Applied Mathematics, Fluid equation, Compressibility, Classical mechanics, Flow (psychology), Geometric group theory, Mathematics, Elasticity (economics), Conservation law, Spatial configuration, Shock wave
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