Displacement of an ideal tracer in a periodic sequence of convergent and divergent sections with allowance for nonlinear effects due to inertia
Abstract
Consideration of the effect of local accelerations and decelerations due to periodic narrowings and widenings of the flow area on the movement of an ideal tracer. The effect of noncylindrical geometry and Reynolds number on the displacement of an ideal tracer was studied on the basis of a numerical integration of the NavierStokes equations by a perturbation method of CauchyCovaleska type. Using the velocities and pressures and periodicity conditions on the velocity distribution at the inlet and outlet as variables, solutions were obtained for steady and periodic flow. The displacement of the tracer was then studied in the numerical plane, using the concept of Lagrangian variables to describe the coordinates of an ensemble of massless particles moving over a fixed Eulerian grid and to define the velocities of the fluid particles. Results are obtained which demonstrate that the effect of noncylindrical geometry and nonlinear effects due to inertia can be studied in an equivalent cylindrical geometry with an elongated velocity distribution.
 Publication:

Academie des Sciences Paris Comptes Rendus Serie B Sciences Physiques
 Pub Date:
 October 1974
 Bibcode:
 1974CRASB.279..407T
 Keywords:

 Convective Flow;
 ConvergentDivergent Nozzles;
 Laminar Flow;
 Numerical Integration;
 Tracers;
 Velocity Distribution;
 Channel Flow;
 Diffusion Theory;
 Incompressible Flow;
 Inertia;
 NavierStokes Equation;
 Viscous Fluids;
 Fluid Mechanics and Heat Transfer