Oscillatory Flow in Curved and Straight Tubes: Transport and Transition.

Transport of soluble material is analyzed for volume-cycled oscillatory flow in a curved tube. The Navier -Stokes equations of motion are solved using a regular perturbation method for small ratio of tube radius to radius of curvature and order unity amplitude over a range of the Womersley parameter. A stream function definition of the lateral velocities is defined to satisfy the conservation of mass equation exactly. A pressure-gradient amplitude is specified to satisfy the fluid volume-cycling constraint imposed. Axial velocity profiles and cross-sectional steady streaming velocity profiles are compared to previous theories and experiments. The convection-diffusion transport equation is similarly solved by a regular perturbation scheme where uniform steady end concentrations and no wall flux are assumed. The time-average axial transport, consisting of the diffusive and convective flux of solute is calculated. There is substantial modification of transport compared to the straight tube case and the results are interpreted with respect to pulmonary gas exchange. A Laser Doppler Anemometer is used to analyze volume-cycled oscillatory flow of a Newtonian viscous fluid in a straight circular tube. The working fluid is chosen to match index of refraction with the Plexiglas test section. The axial velocity is measured at radial positions across the diameter of the tube for a wide range of amplitude A = stroke distance/tube radius (2.4 <=q A <=q 21.6) and Womersley parameter (9 < alpha < 33). Transition to turbulence is detected during the decelerating phase of fluid motion for 500 < R_delta < 875, where R_delta = alphaAsurd2 is the Reynolds number based on Stokes layer thickness. This instability is confined to the viscous boundary layer and does not appear in the inviscid core as reported by previous investigators, unless a source of vorticity such as a hot -wire anemometer probe is resident in the flow.