[Paper Review] The laminar flow instability criterion and turbulence in pipe

S. L. Arsenjev, I. B. Lozovitski+1 more|ArXiv.org|Mar 19, 2003

Coal Combustion and Slurry Processing3 citations

TL;DR

This paper proposes a novel instability criterion for laminar-to-turbulent transition in pipe flow by modeling the fluid stream as a flexible rod undergoing buckling-like instability. The criterion incorporates inlet geometry, pipe length, flow velocity, and physical factors, showing Reynolds number as a local similarity parameter within a broader stability framework applicable to both internal and external flows.

ABSTRACT

The identification of stream in the straight pipe as a flexible rod has allowed to present the criterion expression for determination of transition of the laminar flow regime to the turbulent as a loss of stability of the rectilinear static structure of translational motion of stream in pipe and its transition to the flexural-vortical dynamic structure of translational motion, just as a flexible rod buckling. The introduced criterion allows to take into account an influencing of the inlet geometry, the pipe length, the flow velocity, and also of any physical factors on stability of the rectilinear flow structure. It is ascertained, that Reynolds number is the number of local hydrodynamic similarity and it is displayed that one is constituent part of the introduced stability criterion. The developed approach to a problem of stability is applicable for a problem solving on internal flow and external streamline.

Motivation & Objective

• To develop a physical mechanism explaining the transition from laminar to turbulent flow in straight pipes.
• To model the fluid stream as a flexible rod to derive a stability criterion analogous to structural buckling.
• To incorporate geometric, flow, and physical factors into a unified instability criterion.
• To re-evaluate the role of the Reynolds number as a local similarity parameter within a broader stability framework.
• To extend the applicability of the stability analysis to both internal and external flows.

Proposed method

• Model the laminar flow in a pipe as a flexible rod undergoing translational motion.
• Apply the concept of structural buckling to fluid flow, treating instability as a loss of rectilinear stability.
• Derive a stability criterion based on the transition from rectilinear to flexural-vortical dynamic motion.
• Integrate inlet geometry, pipe length, flow velocity, and physical parameters into the stability criterion.
• Express the Reynolds number as a constituent part of the derived stability criterion, not as an independent parameter.
• Apply the framework to both internal and external flow problems using the same underlying principle.

Experimental results

Research questions

• RQ1 What physical mechanism underlies the transition from laminar to turbulent flow in straight pipes?
• RQ2 How can the fluid stream's behavior be analogized to a flexible rod's buckling instability?
• RQ3 What factors influence the stability of rectilinear flow in a pipe beyond the Reynolds number?
• RQ4 How is the Reynolds number related to the proposed stability criterion?
• RQ5 To what extent can this stability framework be generalized to external flows?

Key findings

• The laminar-to-turbulent transition is interpreted as a loss of stability in rectilinear flow, analogous to the buckling of a flexible rod.
• The proposed stability criterion accounts for inlet geometry, pipe length, flow velocity, and physical factors such as viscosity and density.
• Reynolds number is shown to be a local hydrodynamic similarity parameter, not an independent determinant of instability.
• The criterion successfully explains the transition mechanism by modeling the flow's dynamic structure as flexural-vortical motion.
• The approach is extendable to both internal and external flows, demonstrating broad applicability.
• The model provides a unified framework where instability arises from structural-like buckling of the fluid stream, not just from inertial effects.