Reducing spin-up time for simulations of turbulent channel flow

Abstract

Spin-up of turbulent channel flow forced with a constant mean pressure gradient is prolonged because the flow accelerates due to an imbalance between the driving pressure gradient and total bottom stress. To this end, a method ensuring a time invariant volume-averaged streamwise velocity during spin-up is presented and compared to simulations forced with a mean pressure gradient for both linear and logarithmic initial velocity profiles. The comparisons are made for open-channel flow with a friction Reynolds number Reτ of 500. Additional simulations with Reτ ranging from 1 to 400 are also run to confirm validity of the method for a range of Reynolds numbers. While the method eliminates spin-up time related to approaching the target volume-averaged velocity, spin-up time is still required for the flow to transition to turbulence and reach statistical equilibrium. Therefore, the time evolution of turbulence in response to different initial velocity profiles and random perturbations is investigated. Simulations initialized with linear velocity profiles trigger turbulence and reach statistical equilibrium sooner than those initialized with logarithmic profiles given the same initial perturbations, a manifestation of the increased shear created by linear profiles. The results suggest that, combined with appropriate initial conditions, ensuring a time invariant volume-averaged streamwise velocity can reduce the computational time associated with spin-up of turbulent open-channel flows by at least a factor of five.