On the Localized Transition of Pipe Poiseuille Flow, Part I: The Role of Tensile Force Flow

ABSTRACT: Early turbulence in dilute polymer-solution pipe flows and full-chord laminar flow on suction-controlled wings at Reynolds numbers (Re) up to 2,000,000 evidently markedly deviate from the conventional pipe-flow transition criterion with a critical Re of 2000–2300. Inspired by the spherical-shell membrane-force theory from structural mechanics, this work develops a force-balance model employing a virtual constant-thickness spherical fluid shell to interpret these anomalous laminar-turbulent transition behaviors. For low-Reynolds-number laminar pipe flow, the curvature radius of the virtual fluid layer varies inversely with the pressure gradient. Laminar-to-turbulent transition is hypothesized to take place when the shell curvature radius becomes smaller than the physical pipe radius. This condition defines a candidate critical tensile-force-flow threshold, expressed as twice the product of the fluid viscosity and the maximum pipe velocity, divided by the pipe radius. In general, in laminar pipe flow, the wall shear stress represents the flow-direction component of the tensile force flow. At this hypothesized transition threshold, wall shear stress numerically equals the critical-tensile-force-flow value, which yields qualitative consistency with documented early-turbulence observations. Furthermore, the proposed critical-tensile-force-flow concept offers a physical interpretation for high-Reynolds-number laminar pipe flow stabilized by wall suction. For suction-stabilized laminar pipes, the actual physical pipe may be conceptualized as a subsection of a larger hypothetical, virtual pipe that reaches the critical-tensile-force-flow condition. The real-wall shear stress is attenuated by a factor related to the ratio between the average velocity in the actual physical pipe and its center-line maximum velocity. We emphasize that this threshold is treated as a Newtonian hydrodynamic baseline rather than a universal intrinsic fluid-material property; further well-controlled experimental validation is required to test its general applicability.