Unsteady Laminar Flow in a Circular Tube: A Test of the Hercol (HermitianCollocation) Computer Code

摘要

HERCOL, a computer code for the integration of second-order differentialequations in one space dimension by Hermitian collocation was used to calculate the unsteady velocity profiles for laminar flow in a circular tube. The code was tested for stability and accuracy on the problem for which an analytical solution exists prior to application to a like problem in which the initial and boundary conditions preclude the existence of analytical solutions. The test problem is one in which a pressure gradient is imposed on a fluid initially at rest in a circular tube; the fluid accelerates and at steady state has a parabolic velocity profile. A second example was constructed from the first; a pressure gradient equal but opposite in sign in imposed on the fluid with a fully developed parabolic velocity profile. At steady state, the velocity is again parabolic but in the opposite direction to that at the initial conditions. Excellent agreement with the analytical solution was obtained in the first problem; in the second, the behavior was as expected.