Friction factor estimation for turbulent flows in corrugated pipes with rough walls

Non-metallic flexible pipes are widely used in industry. They are comprised of fabric wrapped over a spiral metal framework. Due to this construction, they respond very well to bending and they are cheaper and much easier to install than metal pipes. Because of the specific construction, the pipe walls are corrugated and the fabric which covers the steel spiral is much rougher than the wall of a metal pipe. In this investigation we are interested in estimating the friction factor for the flow in this type of pipes. Two-equation turbulence models (k -?? and k -!) are used in the computations. The process of deriving these models is presented first. Then we look at turbulent boundary layers and the law of the wall which gives the velocity profile near the wall. Its use as a boundary condition is explained. After the theoretical ideas have been exposed, we look at fully developed turbulent flow in a conventional pipe. Simulations are performed to validate the chosen models, boundary conditions and computational grids. Then a new boundary condition is implemented based on the "combined" law of the wall. It enables us to model the effects of roughness. The new boundary condition is validated by performing simulations of turbulent flow in rough pipes and comparing the computed friction factor to the one given by the Moody diagram. Finally, turbulent flow in periodically corrugated (flexible) pipes is considered. New flow phenomena (such as flow separation) caused by the corrugation are pointed out and the essence of periodically fully developed flow is explained. The friction factor for different values of relative roughness of the fabric is estimated by performing a series of simulations. Conclusions are drawn based on the results of the computations. Some of them are that the k - ?? model performs slightly better than the k - ! model in predicting both regular and separated flow and that the friction factor in a flexible corrugated pipe is mostly determined by the shape and size of the steel spiral, and not by the type of the fabric which is wrapped around the spiral