Mathematical Modeling of Laminar and Turbulent Single-phase and Two-phase Flows in Straight and Helical Ducts

Abstract

The purpose of this research is to investigate numerically the dynamics and heat transfer of laminar or turbulent flows in different media and complicated geometries, including the flow in a composite domain whose central portion is occupied by a clear fluid (turbulent flow) and whose peripheral portion is occupied by a fluid saturated porous medium (laminar flow); a laminar flow of a non-Newtonian fluid in a helical pipe; a laminar flow in a helical pipe filled with a fluid saturated porous medium; a two-phase laminar flow (non-Newtonian carrying fluid and solid particles) in a helical pipe. To model forced convection in a composite porous/fluid domain, the Brinkma-Forchheimer-extended Darcy equation is utilized for the porous region and a two-layer algebraic turbulence model is utilized for the flow in the central region. The effects of turbulence on velocity and temperature distributions as well as on the Nusselt number are analyzed. To investigate a fully developed laminar flow of a non-Newtonian fluid in a helical pipe, an orthogonal helical coordinate system is utilized and the Navier-Stokes and energy equations for the non-Newtonian fluid in this coordinate system are derived. The effects of the curvature and torsion of a helical pipe, the Dean number and Germano number on the velocities, secondary flow and heat transfer are presented. A full momentum equation for the flow in porous media that accounts for the Brinkman and Forchheimer extensions of the Darcy law as well as for the flow inertia is adopted to study the fully developed laminar flow in a helical pipe filled with a fluid saturated porous medium. The effects of the geometry of the helical pipe and the physical properties of the porous medium are investigated. Accounting for the flow inertia is shown to be important for predicting the secondary flow in a helical pipe. For 3D modeling of two-phase laminar flow in a helical pipe, the Eulerian approach is utilized for fluid flow and the Lagrangian approach is utilized for tracking particles. The interaction between the solid particles and the fluid that carries them is accounted for by a source term in the momentum equation for the fluid. The influence of inter-particle and particle-wall collisions is also taken into account.