Analog simulation of particle trajectories in fluid flow

Abstract

This paper presents a detailed account of the analog simulation of particle trajectories in a two-dimensional fluid flow field governed by Laplace's equation. A conductive surface is used as a direct analog of the two-dimensional fluid flow field in conjunction with an electronic analog computer to determine the trajectories of particles in the presence of fluid flow. Emphasis is placed on the concept of accuracy of the particle trajectories as well as error criteria by which trajectory accuracy can be judged; and on the sources of error inherent in their determination. A detailed error analysis is presented in which a suitable error model is derived and certain inaccuracies in the computing equipment are assumed in order to predict their effect on the particle trajectories. An example is presented to illustrate the types and magnitudes of errors that exist in a typical problem. The analog simulation is also used to obtain trajectories in a potential flow field distorted by the presence of a cylinder and the results are then compared to a similar case obtained by other authors using a different approach. These results were comparable, with suitable explanations for the differences.