Suboptimal control for drag reduction in turbulent pipe flow

Abstract

A suboptimal control law in turbulent pipe flow is derived and tested. Two sensing variables ∂p/∂θ|w and ∂vθ/∂r|w are applied with two actuations ϕθ and ϕr. To test the suboptimal control law, direct numerical simulations of turbulent pipe flow at Reτ = 150 are performed. When the control law is applied, a 13–23% drag reduction is achieved. The most effective drag reduction is made at the pair of ∂vθ/∂r|w and ϕr. An impenetrable virtual wall is observed by the controlled wall suction and blowing. The virtual wall concept is useful for analyzing the near-wall behavior of the controlled flow. Comparison of the present suboptimal control with that of turbulent channel flow reveals that the curvature effect is insignificant.