Numerical predictions of turbulent flow and heat transfer in circular pipes using a low Reynolds number two-equation model of turbulence

The present paper is concerned with the numerical simulations of the turbulent flow and heat transfer in circular pipes using a low Reynolds number model for turbulence kinetic energy and its dissipation rate. Unlike the high Reynolds number turbulence models, the present solution procedure requires no special treatments near the pipe walls; i.e., no wall functions are needed to simulate the turbulent flow and heat transfer at the pipe walls. It is well known that the type of the wall function has been criticized on the basis that the obtained solution is essentially dependent on some adjustable tuning model constants. The present low Reynolds number model takes the solution up to the walls without any abrupt changes in the axial velocity and temperature profiles. Finite-volume equations are derived for the conservation equations of the mass continuity, axial and radial velocity components, temperature, turbulence kinetic energy and its dissipation rate. The resulting finite-volume equations are solved iteratively using a tri-diagonal matrix algorithm. The obtained results are considered converged when the errors are less than 0.1 percent. The converged radial profiles of the gas temperature, the axial velocity and the axial profiles of the Nusselt number, mean bulk temperature and wall heat flux are presented for six fixed values of the Reynolds numbers. Moreover, the axial profiles of the Nusselt number are presented for six values of the Reynolds number. The agreement between the present results and the corresponding standard analytical and numerical data is very good.