Análise híbrida do escoamento turbulento em canais via modelos de turbulência de uma equação de transporte

Abstract

The present work consists of a hybrid numerical-analytical simulation of the developing and fully developed turbulent flows inside a parallel-plates channel. The Reynolds equations for the mean flow are solved through the Generalized Integral Transform Technique (GITT) in the boundary layer and streamfunction-only formulations. For turbulence closure, the respectively one-equation turbulence models, and some of their variations, developed by Secundov (1972), Baldwin e Barth (1990), Spalart e Allmaras (1992, 1994) and Menter (1997) were employed. Despite of based on the eddy viscosity concept, as the well-known one-equation k-L turbulence model previously adopted in works that made use of the present hybrid solution methodology, such models do not need any explicit length scale, and therefore are more generals, but only one transport equation for the turbulent viscosity or for a variable directly related to the eddy viscosity. In this sense, some simulations for different Reynolds numbers and different turbulent inlet conditions were developed in order to, in function of the obtained results and the convergence studies of the main potentials involved in the simulations, develop a critically and detailed discussion of the main shortcomings and capability predictions of each turbulence model adopted, such as the non-asymptotic development of the longitudinal velocity component and the friction factor fields. As a consequence of the analysis type performed over each turbulence model investigated and, in addition, due to the excellent numerical quality of the obtained results, the present work extends and consolidates the very important role that the integral transform technique may play in the computational fluid dynamics field meanwhile hybrid methodology.