RANS modeling of the transition of a non-isothermal flow of a Newtonian fluid to a viscoplastic state in a pipe

A mathematical model of the movement and heat transfer of a turbulent non-isothermal non-Newtonian fluid through a pipe wall with a cold surrounding space has been developed and simulated numerically. Fluid turbulence is described in the framework of the isotropic two-parameter k– model. The Newtonian properties of the fluid in the initial cross-sections of the pipe transformed gradually into a viscoplastic non-Newtonian Bingham-Schwedoff fluid state due to heat transfer through the pipe wall between the heated fluid and a cold environment. The value of its streamwise velocity in the axial zone increased significantly when the fluid moved along the pipe. On the contrary, it decreased in the near-wall zone and the height of the region with a zero fluid velocity increased. This occurred due to the viscoplastic properties of a non-Newtonian fluid. The height of the region with a zero fluid velocity in the pipe increased gradually as the non-Newtonian fluid (waxy crude oil) moved through the pipe. A noticeable increase in the level of turbulent kinetic energy in the axial zone of the pipe and its noticeable decrease in its near-wall region were observed. A significant increase in the average dynamic viscosity and yield stress in the near-wall part of the pipe was shown. The boundary of the area of existence of Newtonian properties of fluid was determined. The height of the region with a zero fluid velocity in the pipe increased gradually as waxy crude oil moved through the pipe and reached y/R ≈ 0.1 at x/D = 15.