CALCULATION OF STEADY AND OSCILLATING FLOWS IN TUBES USING A VORTICITY TRANSPORT ALGORITHM

Steady and oscillating axisymmetric tube flows are modelled using a vo rticity transport algorithm. The axisymmetric convective-diffusive Nav ier-Stokes equations are solved using a splitting technique. Axisymmet ric ring vortex filaments are introduced on the walls and subsequently convected and diffused throughout the flow field. An axisymmetric equ ation similar to the Oseen diffusion equation is used to diffuse the r ing vortex filaments. Vorticity is reflected from the tube walls using two techniques. Results are presented for the developing Poiseuille f low and for the developed how in the form of the entrance length and t he axial velocity and vorticity profiles. Good agreement is achieved w ith a finite difference method in the developing region of Poiseuille flow. The developed flow results are compared with the analytical solu tions. The developed profiles of velocity and vorticity have errors of less than 0.3 per cent for both methods of dealing with reflection of diffusion at the bounding surfaces and similar accuracy is obtained f or the velocity profiles in oscillating flow except at the wall. Oscil lating flow is produced with a discretized sinusoidal piston motion. V elocity profiles, boundary layer thickness and entrance length are pre sented for oscillating flow. Good agreement is achieved for low-Womers ley-number non-dimensional frequency. At higher values of this paramet er, flows are inaccurately simulated, because the number of piston pos itions used to discretize the piston motion is inversely proportional to the non-dimensional frequency.