Deformation of a fluid-filled compliant cylinder in a uniform flow

• Published in: Journal of fluids and structures Vol. 25; no. 6; pp. 1049 - 1064
• Main Authors: Yokoyama, M., Mochizuki, O.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.08.2009; Elsevier
• Subjects: Biological and medical sciences; Biomechanics. Biorheology; Compliant cylinder; Coupling problem; Deformation; Exact sciences and technology; Fluid dynamics; Fundamental and applied biological sciences. Psychology; Fundamental areas of phenomenology (including applications); General theory; Membrane; Numerical simulation; Physics; Solid mechanics; Structural and continuum mechanics; Tissues, organs and organisms biophysics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Numerical simulation; Membrane; Deformation; Fluid dynamics; Coupling problem; Compliant cylinder; Membranes; Ductility; Erythrocytes; Cell biology; Aspect ratio; Oscillating flow; Finite element method; Vibrations; Internal flow; Gums; Spring mass damper system; Modelling; Runge-Kutta methods; Mechanical properties; Two dimensional flow; Equations of motion; Biomechanics; Drag; External flows; Mechanical system; Internal fluid; Circular cylinder; Vortex flow; Navier-Stokes equations
• ISSN: 0889-9746; 1095-8622
• DOI: 10.1016/j.jfluidstructs.2009.05.006

We investigated surface compliance effects of a fluid-filled object in flow on its shape and internal flow through numerical simulation. A two-dimensional compliant cylinder containing fluid in a flow is a simple model of a cell, e.g. an erythrocyte, leukocyte or platelet. The thin membrane of the cylinder consisted of a network of mass-spring-damper (MSD) systems, representing its mechanical characteristics. We assumed that the stiffness and damping coefficients were those of latex gum. The two-dimensional flow inside and outside the membrane was obtained by solving the two-dimensional Navier–Stokes equations by using the finite element scheme at Re=400, based on the external flow velocity and diameter of an initial circular cylinder. The deformation of the membrane was calculated by solving the equation of motion for an MSD system by using the fourth-order Runge-Kutta method. The compliant cylinder deformed more if its stiffness was smaller than that of latex gum. The initial circular section of the cylinder became oval, with a flat front and a convex rear. The aspect ratio of the lateral to streamwise axis length of the oval became larger than unity, and increased with decreasing stiffness. The drag coefficient of the oval cylinder became larger than that of the circular cylinder, and increased with decreasing stiffness. The partial vibration at the rear, caused by shedding vortices, induced oscillating internal flows between two antinodes of the vibrating membrane. Since the object with smaller stiffness had higher ductility, velocity fluctuations of the external flow influenced the internal flow of the compliant object through deformation of the membrane.