Numerical modelling of unsteady turbulent flow in smooth-walled pipes:

An efficient numerical model for turbulent friction has been developed for smooth-walled pipe flow. The aim was to develop a new approach to the numerical modelling, eliminating some important approximations and sources of error, such that the method can be applied reliably under a wide range of conditions. A simple two-region model of effective viscosity is used. For short timescales, the turbulence level and effective viscosity distribution are ‘frozen’ in time. The velocity profile is determined numerically for a range of frequencies and viscosity distributions, and this is used to determine the frequency-dependent friction. This is then approximated using simple weighing functions. This turbulence model can be implemented readily in several types of numerical model for pipe flow, including simple lumped parameter models, finite difference/finite element methods, and the method of characteristics.