Quasisteady modeling of periodic turbulent pipe flows

Most numerical calculations of periodic turbulent boundary layers and studies of pipe and channel flows have been based on an employment of turbulence models in a quasi-steady manner, taking into account the same form used in earlier steady-flow calculations, without rigorous justification. The present investigation is concerned with the implications of such a 'quasi-steady' usage, giving particular attention to cases in which the time scale of the externally imposed periodicity is comparable to the characteristic time scale of turbulent fluctuations in the flow. Equations and models are considered along with results, and a comparison with experiments. The investigation suggests that quasi-steady, eddy viscosity-type turbulence models do not correctly describe the ensemble-averaged flow even at moderately large frequencies (frequencies of one order smaller than the turbulent bursting frequency in the flow).