Turbulent Diffusion in the Pipe Flow by the Stochastic Lagrangian Model

In this short paper, we present the results of the numerical simulations of the scalar diffusion fields in a fully developed turbulent pipe flow by using the Lagrangian stochastic process model. The model used here is a Generalized Langevin (GL) model expressed in the cylindrical coordinate system [l]. The GL equation was first proposed by Haworth & Pope [2] in order to model the joint PDF equation of the velocity, and then applied to simulate the velocity and scalar field with the scalar mixing model mainly for self-similar turbulent flows [3][4]. With regard to the velocity field, recently the relationship between stochastic Lagrangian models and second-moment closures has been in detail examined [5], and the extension of the GL model has been also made to include modelling of the near-wall turbulent flow [6]. However, to date, almost no applications of this technique to the scalar diffusion field in a wall turbulent flow and inner flow such as pipe flow have been made.