Transition from laminar to turbulent pipe flow as a process of growing material instabilities

Abstract

Experiments show that a laminar pipe flow starts to change to turbulence at Reynolds numbers around 2000. However, the classical Navier-Stokes theory fails to explain such a transition; according to it the pipe flow should always be stable and laminar. In the present work, it is hypothesized that the transition to turbulence occurs due to material rather than kinematic instabilities of the flow, and the classical Navier-Stokes theory is enhanced with a description of viscous strength. Numerical simulations of the pipe flow with and without the viscous strength are performed. The results show that material instabilities due to the viscous strength gradually develop into a turbulent flow, in agreement with the experimental observations. In the absence of viscous strength, the pipe flow remains laminar in disagreement with experiments. It is concluded that the material instabilities can generally compete with the kinematic ones in the process of transition from laminar to turbulent flow.

Keywords

• Transition into turbulence
• Viscous strength model
• Pipe flow simulation
• Navier-Stokes model