Procedings of COBEM 2005 Copyright c  2005 by ABCM 18th International Congress of Mechanical Engineering November 6-11, 2005, Ouro Preto, MG Numerical Simulation of Turbulence in Open-Channel Flows Daniel Vieira Soares Departamento de Engenharia Mecânica - Universidade de Brasília - UnB Campus Univeritário Darcy Ribeiro, CEP 70910-900, Brasília, Brasil danielvs@linkexpress.com.br Juliana Braga Rodrigues Loureiro Programa de Engenharia Mecânica (PEM/COPPE/UFRJ) C.P. 68503, 21945-970, Rio de Janeiro, Brasil jbrloureiro@mecanica.coppe.ufrj.br Átila Pantaleão da Silva Freire Programa de Engenharia Mecânica (PEM/COPPE/UFRJ) C.P. 68503, 21945-970, Rio de Janeiro, Brasil atila@mecanica.coppe.ufrj.br José Luiz Alves da Fontoura Rodrigues Departamento de Engenharia Mecânica - Universidade de Brasília - UnB Campus Univeritário Darcy Ribeiro, CEP 70910-900, Brasília, Brasil fontoura@unb.br Abstract. The main goal of this work is to provide a performance analysis of a numerical simulation methodology in solving open-channel turbulent flows with separation of the turbulent boundary layer. To accomplish this, a selected experimental test case was chosen, a turbulent open-channel flow over a hill, where the detachment of the turbulent boundary layer occurs due to the presence of low intensity adverse pressure gradients. For example, this case is specially important to the research of turbulent mechanisms present in atmospheric flows over irregular terrains or obstacles, or river flows past submerged rocks. The mean equations of conservation of mass and momentum are obtained via the classic κ - ε model of Jones and Launder. Spacial discretization is done by P1/isoP2 finite element method and temporal discretization is implemented using a semi-implicit sequential scheme of finite difference. The coupling pressure-velocity is numerically solved by a variation of Uzawa’s algorithm. To filter the numerical noises, originated by the symmetric treatment of Galerkin’s method to the convective fluxes, a balance dissipation method is adopted. The remaining non- linearities, due to the use of velocity laws of wall, are treated by a minimum residue method. The numerical results obtained with the use of four different velocity laws of the wall are compared to the available experimental data of the considered flow. Keywords: turbulence, separating boundary layer, open-channel flow, laws of the wall, finite-elements method 1. Introduction The objective of this work is to test the numerical performance of different laws of the wall in cases of open-channel turbulent flows with separation of the boundary layer, testing the methodology shown by Soares and Fontoura Rodrigues (2003 and 2004) of numerical simulation using laws of the wall. To accomplish this, a selected experimental test case was chosen, a turbulent open-channel flow over a hill, where the detachment of the turbulent boundary layer occurs due to the presence of low intensity adverse pressure gradients, intercalated between two regions of stream-wise pressure gradients. This case is specially important to the research of turbulent mechanisms present in atmospheric flows over irregular terrains or obstacles, or river flows past submerged rocks, all of which have several engineering applications, from seacraft design to atmospheric and climate forecasts. The algorithm to be tested, Turbo 2D, is a combination of the numerical simulation methodology using finite elements, proposed by Brison et al. (1985), with an error minimization method adapted to a finite elements, for the simulation of turbulent wall flows with non-linear boundary conditions, proposed by Fontoura Rodrigues (1990 and 1991), using the classic κ - ε turbulence model of Jones and Launder (1972). By applying Galerkin’s method for finite elements to the calculation of convection dominant flows, numerical oscillations without physical meaning can appear. This fact occurs due to the usage of Galerkin’s method, that gives a symmetric treatment to the flow modeling, which is a non symmetric physical phenomenon. To lower the tendency of numerical oscillation, a balancing dissipation method, proposed by Huges and Brooks (1979) and Kelly et al. (1980) and implemented by Brun (1988), is used in Turbo 2D. The results obtained with simulations using four different laws of the wall, implemented in Turbo 2D, are compared to the experimental data available from the test case of Loureiro (2004): a turbulent open-channel flow over an abrupt hill.