Numerical Simulation of the Entrance Length in a Laminar Pipe Flow at Low Reynolds Numbers

Xiaoli Qi, Qikun Wang () and Lingjie Ke
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Xiaoli Qi: School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
Qikun Wang: School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
Lingjie Ke: School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

Mathematics, 2025, vol. 13, issue 8, 1-13

Abstract: According to Prandtl’s boundary layer theory, the entrance length refers to the axial distance required for a flow to transition from its initial entry condition to a fully developed flow where the velocity profile stabilizes downstream. However, this theory remains applicable only under the assumption of Re ≫ 1, while its validity diminishes under low-Reynolds-number conditions. This study utilizes OpenFOAM based on the finite volume method to numerically examine Newtonian and viscoelastic fluids in a laminar circular pipe flow. The objective is to determine the range of Reynolds numbers for which the differential equations from within the Prandtl boundary layer theory are strictly valid. Additionally, the study explores the effects of Reynolds numbers ( Re ) ranging from 50 to 100, s solvent viscosity ratio ( β) fixed at 0.3 and 0.7, and Weissenberg numbers ( Wi ) ranging from 0.2 to 5 on the entrance length and friction factor for the Oldroyd-B model. The results indicate the presence of a lower Reynolds number that impedes the attainment of the outcomes predicted by the Prandtl boundary layer theory for the entrance length. The inertia effect, the increase in solvent viscosity contribution, and the elastic effect exhibit a linear relationship with the entrance length and friction factor.

Keywords: Reynolds number; laminar pipe flow; Oldroyd-B model; entrance length (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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