Laminar Pipe Flow Instability: A Theoretical-Experimental Perspective

This paper revisits the theoretically predicted inherent stability of fully developed laminar pipe flow, which remains unconfirmed by experimental evidence. A recently developed theory of pipe-flow stability/instability addresses the gap between experimental observations and classical theoretical predictions by accounting for a parallel secondary flow through the pipe’s roughness layer that accompanies the main stream. This secondary flow alters the near-wall velocity profile in the rough-wall region, creating an inflection point that promotes shear-driven instabilities and triggers the laminar-to-turbulent transition. A stability factor $S=D_c/D$ is introduced, where D is the nominal pipe diameter and $D_c$ refers to the critical pipe diameter. The pipe flow remains laminar and stable for $S>1.0$, and becomes unstable for $S<1$. Various experimental findings are theoretically derived, and the laminar-to-turbulent transition is identified at $S=1.0$. Particular attention is paid to the dependence of flow transition on both pipe diameter and pipe length. Rather than relying on a critical Reynolds number $R{e}_c$, this study proposes the critical pipe diameter $D_c$ as the key parameter governing the laminar pipe flow instability, where $R{e}_c$ refers here to the condition-dependent threshold at which laminar pipe flow becomes unstable and transition to turbulence occurs. The present analysis further suggests that instability arises only if the pipe length L exceeds a critical threshold $L_c$, that is, $L>L_c$. The theoretical treatment presented provides deeper physical insights into the onset of laminar pipe flow instability including the phenomenon of reverse transition. It also distinguishes between natural and forced flow transitions, providing a refined understanding of the transition process. Finally, suggestions for future experimental work are made to further validate or challenge this new theoretical perspective on pipe flow instability.