Modeling of Thermal Two Dimensional Free Turbulent Jet by a Three Layer Two Time Scale Cellular Neural Network

Abstract

A three layer Cellular Neural Network (CCN) is used to model the velocity and temperature profiles in a two dimensional turbulent free jet. CNNs are a class of neural networks which are adapted for Integrated Circuits (ICs) and can process data in parallel asynchronously at very high speeds. To implement the CNN model together with an appropriate discretization scheme variable mesh size in vertical direction was also considered. As CNN operates in continuous-time and the propagation speeds of the velocity and temperature fronts are in general unequal, two different time scales were accordingly used. These time scales were set such that the ratio of the time constants of the corresponding momentum to thermal layers in the CNN matched the turbulent apparent eddy to temperature diffusivity ratio, or namely the turbulent Prandtl number. The results were compared with computational fluid dynamics similarity based solutions and indicate acceptable agreement. From the results one can justify the use of neural networks, as a powerful new tool in the fluid dynamics problems, to tackle such numerically extensive and expensive phenomena as turbulence.