Enzo O. Macagno

Computational and experimental study of a captive annular eddy

Results of calculations and experiments on the flow of a viscous liquid through an axisymmetric conduit expansion are reported. The streamlines and vorticity contours are presented as functions of the Reynolds number of the flow. The dynamic interaction between the main flow and the captive eddy between it and the walls is analysed, and it is concluded that, for laminar flow, the main role of the eddy is that of shaping the flow with a rather small energy exchange.

Historico-critical review of dimensional analysis

Abstract The history of dimensional analysis is examined critically from the first notions about dimensions in old civilizations to the powerful methods of recent times. Dimensional analysis, as we know it and use it today, has been in active use for almost a century, although the basic ideas were published one hundred and fifty years ago. The elementary notions have a much longer history, because some of them were tacitly applied whenever a system of measurement of physical quantities was invented or put to use. This aspect has been keenly analyzed in the early 1920s by P.W. Bridgman, who used it in establishing one of the two basic theorems of dimensional analysis. The other theorem had been derived some thirty years before by A. Vaschy, and was rediscovered once or twice, and given more rigorous proofs by several mathematicians. Dimensional analysis remains a method which is most useful in areas in which knowledge is developing through an intermediate stage at which the basic laws are already known, but there is still a lack of powerful methods of solution. This study has been restricted to dimensional analysis proper, leaving out as much as possible the akin topics of similitude, modeling and simulation. Some rather recent developments of dimensional analysis have not been examined because of the obvious reason of their lack of historical prospective.

Finite-element analysis of flow induced by contractions like those of the intestine

Abstract After a brief description of the wall movements of the small intestine, the simplifications introduced to allow an analysis of the fluid mechanics of intestinal contractions are described. These simplifications, bearing mainly on the fluid properties, led to the use of the biharmonic equation as the governing equation of fluid flow. This is considered valid without excluding essential flow features. The kinematics of the wall cannot, however, be simplified so radically without too much loss, so that the use of numerical techniques was unavoidable. The versatility of the finite element method led to adoption of that procedure. It was necessary to make some changes because of the complexity of the flow patterns. This was accomplished by the careful use of the fifth-degree polynomial. It was thus possible to obtain reliable flow patterns, accurate velocity profiles and values for the flow rates. It was shown that isolated propagative transverse contractions over a finite length of the conduit can pump. The results of the numerical integrations are given in the form of velocity profiles, streamlines, and pumping characteristics. Although, so far, these results are for two-dimensional channels, the results represent a general behavior, so that further work with circular tubes should yield similar results.

Pressure, Bernoulli Sum, and Momentum and Energy Relations in a Laminar Zone of Separation

The pressure field, the Bernoulli‐sum variation, and the different terms of the impulse‐momentum and work‐energy relations have been determined computationally for a conduit expansion of 2:1 and a Reynolds number of 48 in the narrow part of the conduit. The procedure used was the integration of an explicit discretized form of the Navier‐Stokes equations. The calculations were carried out with an IBM 7044 electronic computer. It was found that some terms of the differential and integrated forms of the basic equations were relatively small. The integrated form of the work‐energy relation can be simplified to only three of its terms. The role of the eddy was found to be essentially that of shaping the main flow, the exchange of momentum and energy with the main flow being rather small.

Numerical integration of the time-dependent equations of motion for taylor vortex flow

Abstract A method is presented for the finite difference solution of the equations of fluid motion. The complete Navier-Stokes equations are expressed in terms of tangential velocity, vorticity and stream function. The transformed equations are solved using an alternating direction implicit scheme. The classical problem of hydrodynamic stability of the rotational Couette flow is solved in two dimensions. Comparison with other numerical and experimental works shows that the method reported here is computationally stable, even when used with coarse grids and relatively large time increments.

Computational Study Of Accelerated Flow In A Two-Dimensional Conduit Expansion

The accelerated flow of a viscous fluid due to a suddenly established discharge in a two-dimensional conduit expansion has been determined by numerical integration of the governing differential equation. The complete form of the equation for diffusion and convection of vorticity was employed. The Reynolds number of the flow, based on the prescribed disharge, was 200. The growth of the separation zone, assuming symmetric flow, was determined. Flow and vorticity pattern were calculated at short interval of time; a selection of those pattern is presented, as well a curves showing the variation with time of the principal kinematic characteristics of the unsteady flow through the expansion.

Nonlinear behavior of line vortices

A simple model is formulated following classical lines and used to investigate the decay of line vortices in which both self‐induced and ambient turbulence may exist. The effect of molecular viscosity is included, since it may be important at certain times and in certain regions of the vortices. Circulation overshoot, predicted for the first time by Saffman, is also predicted by this model when self‐induced turbulence is taken into account. This occurs even if no trace of overshoot is present initially. Experimental data of Focke, which exhibit overshoot, are used to test the model. The presence of a logarithmic portion in the circulation profiles of turbulent vortices is discussed critically.