Nonlinear and viscous effects on wave propagation in an elastic axisymmetric vessel
Journal
Journal of Fluids and Structures
Journal Volume
27
Journal Issue
1
Pages
134-144
Date Issued
2011
Author(s)
Abstract
In this paper, a power series and Fourier series approach is used to solve the governing equations of motion in an elastic axisymmetric vessel with the assumption that the fluid is incompressible and Newtonian in a laminar flow. We obtain solutions for the wave speed and attenuation coefficient, analytically where possible, and show how these differ under a number of different conditions. Viscosity is found to reduce the wave speed from that predicted by linear wave theory and the nonlinear terms to increase the wave speed in comparison to the linear solution. For vessels with a wall stiffness in the arterial range, the reduction in the wave speed due to the viscous terms is approximately 10% and the increase due to the nonlinear terms is approximately 5%. This difference between the linear and nonlinear wave speeds was found to be largely constant irrespective of the number of terms considered in the power series for the velocity profile. The linear wave speed was found to vary weakly with stiffness, whilst the nonlinear wave speed was found to vary significantly with the stiffness, especially at low values of stiffness. The 10% variation in the wave speed due to the viscous terms was found to be constant with wall stiffness whilst the 5% variation due to the nonlinear terms was found to vary with wall stiffness. The importance of the number of terms considered in the power series is discussed showing that only a relatively small number is required in the viscous case to obtain accurate results. ? 2010 Elsevier Ltd.
Subjects
Attenuation coefficient
Axisymmetric
Governing equations of motion
Linear solution
Linear wave theory
Linear waves
Newtonians
Non-Linearity
Nonlinear terms
Nonlinear waves
Power series
Velocity profiles
Viscous effect
Wall stiffness
Wave speed
Control nonlinearities
Fourier analysis
Fourier series
Harmonic analysis
Laminar flow
Speed
Stiffness
Viscosity of liquids
Viscous flow
Walls (structural partitions)
Wave equations
Wave propagation
Navier Stokes equations
Type
journal article