Numerical calculation of internal flows with curvature

Flow in curved pipes involves secondary flows and possibly streamwise separation. An efficient numerical scheme yielding reliable predictions for such flows is presented. This is accomplished by using a simple turbulence model that reproduces the main features of the flow in curved pipes and fits with a numerical scheme suitable for such complex flow geometries. The numerical scheme used in this study is called Bodyfit and it solves the three dimensional elliptic equations of motion using the technique of boundary fitted coordinate transformation. A two equation K-epsilon turbulence model is used. The distribution of the eddy viscosity is calculated by solving two partial differential equations for the turbulence kinetic energy and its volumetric rate of dissipation simultaneously with the set of basic equations of momentum and continuity. The finite difference equations are solved using a cell by cell successive over-relaxation method (SOR). Computations were made for both laminar and turbulent flows in straight and strongly curved pipes of circular cross section. The numerical scheme gives a table solution for mean velocity and turbulence quantities. A modified pressure equation is recommended.